> zyObjbj]W]W?=?=)%8\#II"kkkFFFZFFFFFkk~~~Fkk~F~~~kPpq~0#~'"~'"~'"~4FF~FFFFF~FFF#FFFF'"FFFFFFFFF?K: SUSY in the Sky with Diamonds.
Rinat M. Nugayev, Tatarstan Academy of Sciences, Kazan 420049, Volgogradskaya 49,Russia.
Abstract. The host of SUSY(supersymmetry) based string theories is considered. Superstrings are comprehended as possible candidates on Quantum Gravity basic objects. It is argued that superstring theories constitute mainly mathematical progress and can reconcile general relativity with quantum field theory at best. Yet they cannot provide the genuine synthesis. Superstring unification of all the four forces at hand is a formal one . It is contended that genesis and proliferation of superstrings can better be described not by philosophy of science models but in terms of modern sociology of science. The formal character of gravity and quantum fields fusion and the lack of experimental verification make the transition to superstring theories ad hoc in Lakatosian standards. Possible way of explanation is proposed based on social interests conception of Andrew Pickering.
Key words: superstrings, unification, KaluzaKlein, sociology of science
Lucy in the sky with diamonds, Follow her down to a bridge by a fountain where rocking horse people eat marshmallow pies, everyone smiles as you drift past the flowers, that grow so incredibly high. The Beatles.
INTRODUCTION. As is wellknown, the scientific research programme of adequate superstring theory construction had been proposed already. Its hard core contains the following statements. (i) The carriers of the fundamental interactions are nonlocal. (ii) Interrelations between bosons and fermions are described by the Supersymmetry Principle. (iii) Spacetime is multidimensional in Theodore Kaluzas sense. At first the principle of nonlocality of the carriers of interaction occured in hadronic physics. Gluonic fields appeared to be concentrated along the lines that connected quarks. All these brought to the pictures of mesons consisting of onedimensional strings connecting a quarkantiquark pair . Inspite of some obvious successes, the string theory development met with difficulties. According to the most dangerous one , the spectrum of the particles predicted by such theories should contain the tachions (that propagate faster than light).On realizing that, Scherk & Schwartz proposed a hypothesis that the spacetime dimension is equal to 10.It had changed the programmes hard core significantly. The heuristic was altered by the assertion that all the unification should be done in full analogy with that of Theodore Kaluza by putting all the new fundamental interactions into new dimensions. It had eliminated the old difficulties but created the new ones. The aim of my paper is to strengthen arguments in support of the proposition that the genesis and character of the newly discovered difficulties cannot allow one to declare that the global theory unifying all the four basic interactions have been already created. Correspondingly, the first part discusses the merits and drawbacks of the original KaluzaKlein theory, outlining the normative unificationist standards, and the second one deals with the difficulties occuring when this theory is generalized to include all the existing interactions.
PART ONE.THE GENUINE KALUZAKLEIN THEORY. In 1921 the German mathematician Theodor Kaluza achieved an elegant unified theory of gravitation and electromagnetism by assuming that spacetime is really 5dimensional with one timelike and four spacelike dimensions. The main merit of the theory consisted in the possibility of treating of the newly born geometrical quantities with
the electromagnetic field potentials. All these was achieved in the following way. The line element is ds2 = gijdxidxj, where for 5dimensional spacetime i,j = 1,2,3,4,5. The metric tensor gij is a matrix consisting of a usual 4dimensional metric tensor g(( ((,(=1,2,3,4),two vector fields A( and A( and very unpleasant  dark and obscure  component G55. After putting it equal to 1 and postulating the cylinder condition according to which the usual 4dimensional metric tensor should have a vanishing derivative with respect to the newly introduced fifth dimension both vector fields A become very much alike the 4potentials of the electromagnetic field. At the same time 5dimensional Cristoffel symbols that contain the first derivatives with respect to all the 5 coordinates appear to be consisted of 4Cristoffel symbols that are analogous to gravitational field stresses and of the Cristoffel symbols that contain the index 5 .The latter remind us of the electromagnetic field stresses. If we identify them with the electromagnetic stresstensor F((, we can derive some interesting consequences that were called by the enthusiasts the KaluzaKlein miracles.
Let us consider them in more detail.
1. The first miracle can be obtained if one equates the5velocity of a particle dx5/ ds to e/m, where e is particles charge and m its mass. Then 5dimensional geodesic equations appear to consist of 4+1 equations. The first four of them are usual equations of motion of a charged particle in the gravitational field in general relativity.
2. The Basic Miracle. 5dimensional Einstein field equations Rij  Rgij=(Tij (where Tij is now exclusive of electromagnetism) reduce to the usual Einstein equations in 4 dimensions and the usual Maxwell equations , and, alas, to the unpleasant equation on G55, (which does not deserve attention of an inventor of unified field theory). There are two more miracles  the appearance of the electromagnetic stresstensor in the right side of the equations and the explanation of the electromagnetic field gauge invariance. But they appear too modest in comparison to the Basic Miracle that attracted even Einstein for several decades of his life. Kaluzas original inspiration was given a firmer basis by Oscar Klein in 1926  mainly in geometrical respects  and finally the bizarre creation was called the KaluzaKlein theory. Besides Einstein, the theory was developed further by Viktor Fock, Jacob Frenkel and Louis De Broiglie. Hence the attraction of the theory had many ups and downs until the 80th when Scherk & Schwartz made a bestseller out of the old physical anecdote. However many (mostly heroic) efforts devoted to the elaborating the theory had revealed some drawbacks pointing out that the hypotheses of Klein and Kaluza made the unification programme too ad hoc.
(1) Why one adds to 4 only one dimension? And not two? Or more?
(2) The cylinder condition is of very artificial origin: ( g((/(x5 =0
Why should the 4dimensional metric tensor with components describing the gravitationalfield stresses in all the points of spacetime obey such a tough condition?
(3) Why the fifth dimension is not observable? And why it is the fifth dimension that is not observable? And not the third one? Kleins earlier suggestion that spacetime be periodic in the new fifth dimension and that 5spacetime is to be thought of as homeomorphic to a tube, the direct product of 4spacetime by a circle with radius x5 satisfying 0 ( x5 ( 2(r5 is not the real explanation .It is just an expression
of the fact that the fifth dimension is closed. In the KaluzaKlein approach one simply asserts that the radius r5 of the circle is very small  only a few orders of magnitude larger than the Planck length hG/c ( 1.6 x 1033 cm. Hence the fifth dimension is not observed in everyday experience due to an ad hoc hypothesis. Einsteins own dictum  one
must explain why the continuum is apparently restricted to four dimensions  is not satisfied in the KaluzaKlein theory.
(4) How should the G55 component of the metric tensor be interpreted? In the most general case this component represents the scalar field analogous to a Coulomb one. Brans & Dickes efforts to introduce in a consequent way this field into General Relativity were not fruitful. They did not provide any new result if not to consider the assertion that the fields coupling constant is too negligible to be measured by modern experimental devices. Moreover, this component interpretation a la Brans& Dicke is new ad hoc hypothesis. But if one (as Kaluza first did) asserts that G55 = 1 this will result in wild physical consequences (see Vladimirov,1989, for details). Critical arguments (1)  (4) can be summarized in the following way. KaluzaKlein unification of gravitation and electromagnetism by assuming that spacetime is really 5dimensional and identification of the newly obtained geometrical quantities with electromagneticfield potentials is too formal to be taken seriously. To say that gravitational and electromagnetic fields are different parts of the same metric tensor so that 5dimensional Einstein equations can be reduced to 4dimensional Einstein equations and 4dimensional Maxwell equations is to say that gravitational and electromagnetic fields are of tensor origin. But the latter proposition is trivial. Einsteins and Maxwells equations were obtained before the KaluzaKlein theory. This theory tells nothing new neither to experimentalists nor to theoreticians. Hence the KaluzaKlein theory represents ad hoc1 and ad hoc2 hypothesis in Lakatosian terms in scientific research programme of unified field theory construction. Many years ago Richard Feynman sarcastically noted (in Feynmans Lectures, as far as I know) that it is quite easy to write out the most profound and fundamental equation that represents the most general physical law that unifies all the known interactions. The law is ( = 0 where the operator ( and function vary for any new field under consideration. For instance, for classical mechanics (=1 and =F  ma, for classical electrodynamics ( is DAlemberts operator and are field quantities, etc. Why is this unification formal?  Because any real  and not formal  unification should result in construction of the basic model of the process under consideration (see Stepin,1976, for instance).Having had rationally reconstructed (together with Lev Tomilchik) the process of electricity, magnetism and theory of light fusion, Stepin did notice some peculiarities of the unification process, that have general significance for any process of scientific synthesis. They were those peculiarities that had provided the Maxwell theory victory over the rival programme of Ampre and Weber. The properties of any successful scientific synthesis can be summarized in the following way.
(i) Any mature scientific theory is a set of propositions describing the relations between different sets of abstract theoretical objects. The abstract objects of any mature theory belong either to a subset of basic objects (called Fundamental Theoretical Scheme of FTS) or to a subset of derivative ones (called Partial Theoretical Schemes or PTS).The latter are constructed from the FTS by some rules belonging to a certain paradigm (in Kuhns sense).Hence the resulting theory should unify not basic laws only, but the systems of theoretic objects as well.
(ii) The objects of the global system should be operationally defined through the ideal measurement procedures. The connection to lowerlevel abstract objects should be specially disclosed. (iii) The abstract objects of the unifying global system should contain the properties that did earlier belong to various objects from different systems of lowerlevel theories. Any violation of (i)  (iii) should violate the rigidity of the levels connection and consequently should lead to decrease of the unifying theorys predictive power. Indeed, what is the cause of this power? If a mature theory is not a direct generalization of empirical data, how can it predict the results of new experiments that are not even performed? How can a mature theory forecast future? According to Stepin (1976), this opportunity is based on the rigid connection between the theoretical basis and real experiments. The link of the basis with experiments is intermediated by the systems of derivative objects. Any basic objects represents the characteristic features of the relations of the derivative objects that belong to the lower level of theoretical objects organization. Hence to give an operational definition of a basic object is to describe idealized measurement operation, a gedankenexperiment, but not the real one. For instance, the operational definition of electric field density J is given not by the description of real measurements. It is given by the description of relations of Maxwells theory abstract objects of electric field at a point and test charge. But these abstract objects are the entities of the partial theoretical schemes of Maxwells theory. And their operational status is determined now by real, and not by ideal, measuring operations. For example, the test charge is determined through such an action of a massive charged body on the other, when the reciprocal influence of the second body on the first can be neglected. The bond between the PTS level and the level of empirical schemes is installed because all the PTS are the idealized schemes of real interactions observed in real experiments. So, all the bonds between all the levels of a mature theory are rigid ones. This rigidity allows one to connect a prediction referring to the upper level with all the levels of a mature theory. Hence it allows one to construct an experimental device to check the prediction. A new result, obtained to the development of mathematical apparatus, immediately influences all the levels of a mature theory. Hence a theory can predict, and the predictions can be verified. Consequently, introduction of operationallyindefinite abstract objects should lead to decrease of the predictive power.
The proponents of KaluzaKlein theory can argue that (i)  (iii) belong to the classical stage of physics development. Modern physics began with Einsteins reconciliation of electrodynamics, mechanics and thermodynamics in 1905 (Nugayev,1996) and his unification of Special Relativity and Newtonian Theory of Gravity. Indeed, Special Relativity and the Early Quantum Theory were created within the same programme of statistical mechanics, thermodynamics and maxwellian electrodynamics reconciliation. Quantum and relativistic revolutions were simultaneous since they had common origin  the clash between the fundamental theories of the second half of the 19th century that constituted the body of Classical Physics. The revolution s most dramatic point was Einsteins 1905 photon paper that laid the foundations of both Special Relativity and Old Quantum Theory. However, Einsteins programme constituted a progressive step in respect to its rivals not because it could explain more facts or was more mathematical. It was high than its rivals because it superseded them operationally. The abstract object ether was introduced into the reductionist programme of Lorentz, Langevine and Wien as a carrier of electromagnetic oscillations. It is a vivid example of operationally indefinite object. No physical experiment could determine the motion through ether. This construct was introduced into the system of abstract objects of Lorentzs theory not due to certain generalizations of measuring operations. It was introduced for the construction of mechanical basis from that of electrodynamics. The material points (the particles) were to be considered as ether perturbations, whereas the forces acting on them were to be determined via the tensions of the ether. Of course in the long run the operational virtues of Einsteins programme resulted in empirical successes. The proponents of KaluzaKlein theory can point at General Relativity as on paradigm of theory construction common for XX century. However, the counterargument can be put forward according to which General Relativity creation has nothing to do with mathematical hypothesis method. In reality this theory was constructed by gradual fusion of empirical and consequent partial theoretical schemes (Nugayev,1987).General Relativity consists not only of Einsteins equations. It includes the socalled weakfield approximation in General Relativity, and Newtons Theory of Gravitation as well. Thus, Einsteins special and general relativities were modern but they did not violate (i)(iii). Modernity in physics had culminated in creation of Quantum Electrodynamics. This period is characterized by the domination of mathematical hypothesis method , when one tries to guess the basic equations or the basic unifying laws with a help of such regulative principles as Beauty, Simplicity, etc. And only after establishing the basic laws one has to provide their empirical justification and to link the system of basic objects to those of the lower level. The most vivid example is creation of Quantum Electrodynamics when special BohrRosenfeld idealmeasurement operations were elaborated. However, the Modern Stage had ended up with the World War II, and the PostModern stage began. All the 3 basic stages of postmodern physics  the electroweak theory of Weinberg & Salam, Quantum Chromodynamics and Grand Unification Theories (or GUTs) & SUSY approach culminating in superstrings  can be described as partial violations of (i)(iii) rules of unification. These deficiencies are still eliminated due to the physicists collective efforts.
Even SalamGlashowWeinberg synthesis of weak and electromagnetic forces, rather innocent in comparison with bold speculations of SUSY theories, was a success only in some limited domains. Alas, the simple conjunction of Higgs mechanism with earlier electroweak gauge models was a serious defeat. These and similar shortcomings of the SalamWeinberg model showed themselves up in the artificial character of their predictions. They were too ad hoc. Let me take as an example the discovery of neutral currents. Thus, in both branches of neutrino physics  bubble chamber and electronic experiments  the pattern was the same. The 1960s order, in which a particular set of interpretative procedures pointed to the nonexistence of the neutral current, was displaced in the 1970s by a new order, in which a new set of interpretative procedures made the neutral currents manifest. Each set of procedures was in principle questionable, and yet the HEP community chose to accept first one and then the other. Why did this transformation come about?(Pickering,1984, p.193). As for eminent Quantum Chromodynamics, the following quotations are especially appropriate here. It is now fashionable to attach to everything the label predicted by QCD. In fact, despite favorable auguries, the confinement problem has not yet been solved and there are no rigorous results from QCD for hadron spectroscopy (Hey, 1979,p.7). Or, in more strong terms: The use of Quantum Chromodynamics (QCD) in treating the hadronic world has become an overwhelming trend in particle physics... Perhaps it is for the first time in the history of physics that a theory which is neither precisely defined nor proved to have the right to exist as a consistent theory has become so popular (Dokshitzer, Dyakonov & Troyan,1979). The single major prediction of Grand Unification Theories involved the electroweak mixing angle (w. In SU(5) Georgi &Glashow model Sin2(w was first predicted to be equal to 3/8.However, some additional theoretical work showed that matters were not so simple. Heroic 19741979 efforts diminished the number of epicycles to 0,20 that could be now compared with experimental value of 0,23.
INVESTIGATING THE WITHCHES CAULDRON: SUPERSYMMETRIES,SUPERGRAVITY, SUPERSTRINGS AND ALL THAT. As is wellknown, supersymmetry is a symmetry between bosons and fermions. Even in the simplest supersymmetric theory the usual 4dimensional spacetime is enlarged to form the superspace any point of which has 8 coordinates: 4 usual x,y,z,t and four new ones belonging to the socalled Grassmans algebra. In the first approximation the usual coordinates correspond to bosons, and the Grassman ones correspond to fermions. If the usual spacetime admits 10parameter Poincare group, the superspace admits 14parameter enlarged Poincare group in which to the usual transformations supertranslations are added. In supersymmetric theory all the fields are exchanged on superfields that depend, in the case of the simplest supersymmetry, upon 8 variables, and in the case of Nenlarged supersymmetry  upon 4+4N variables. Supersymmetric lagrangian , as always, is defined in the form containing invariant square expressions composed from superfields first derivatives along all the 8 coordinates. Superaction is defined as an integral of the lagrangian along all the variables. All these was about the global supersymmetry. The next step in the theory development should consist in localizing the supersymmetry, i.e. in introducing the dependence of supertranslational parameters upon the usual 4coordinates.Just as the localization of usual Poincare group parameters leads to general relativity creation, localization of 14parameter enlarged Poincare supergroup results in supergravity creation. The number of additional variables N varies in this theories from 1 to 8.Maximally enlarged N=8 theory of supergravity consists of one spin 2 field ,eight fields with spin 3/2,28 spin 1 fields, and 70 spin 0 fields. It is no surprise that supergravity fans did not decide yet what one ought to do with all these treasures and with what fields should the supermultiplets be identified. And who can provide the superselection rules then? Nevertheless the process had begun and supergravitational KaluzaKlein theories with n usual coordinates and m Grassman coordinates were proposed. Especially interesting the supergravity theories appeared in 11 dimensions, since 11 is the minimal number necessary for introducing the gauge Great Unification Group SU (5) x SU(2) x SU(1).11 is the least spacetime dimension to include electromagnetic, strong and weak interactions. Moreover, namely 11 dimensions admit compactification of additional 7 dimensions. But how? Let me consider the methods of KaluzaKlein supergravity theories construction. This theories are created by simple generalization of 5dimensional KaluzaKlein theories on the case of N = 4+D dimensions. However all the method is based on the assumption that Einstein equations are valid for D dimensions. The ground state from the very beginning is chosen as 4 x BD, where BD admits a group of isometries generated by D Killing vector fields, and not as 4+D..Yet the latter expression should be valid to make the unification correct. Expressions for metric are derived. In complete analogy with 5dimensional 4x S1, group of isometries BD should show itself up as group of gauge symmetries of the fields existing within 4.Indeed, KaluzaKlein genuine approach was demonstrated in the first part of this paper. The electromagnetic fields gauge invariance appears to be a consequence of the fifth coordinate special role. Gauge invariance appears to be an expression of 5dimensional symmetry in 4dimensional world. Spacelike Killing vector field (/(x5 generates isometries that appear as the U(1) gauge symmetry in 4. Hence in the most general case one can always choose D so as to unify gravity with any gauge group. They say that D admits the isometries group G generated by D Killing vectors. In 4dimensional spacetime G will look like nonabelian gauge group. Gauge invariance is a simple spacetime invariance in multidimensional spacetime. In complete analogy with KaluzaKlein theory, the metric tensor in 4+D dimensions can be written as 4dimensional metric plus 4D components of gauge field quantities plus a pile of scalar fields. 4 x D will be a superspace now. Obviously the opportunity of such a representation of the metric in 4+D dimensions is due to the generalized cylindric conditions .They appear now as specific restrictions shaping group generators, i.e. the Killing vectors. Namely they let the generalized lagrangian to be written as a sum consisting of two parts (Chyba,1985).The first part is a usual lagrangian of a free field in 4 dimensions and the second one is the YangMills one describing the gauge fields under consideration. From this lagrangians by standard quantumfield methods the 4dimensional Einstein equations, as well as the YangMills ones (including the equations of Maxwell, KleinGordonFock, Dirac et al.) are derived. Since the procedure described is a simpleminded generalization of 5dimensional case, it is no wonder that all the KaluzaKlein miracles remain. But all the drawbacks remain too. And the new ones appear: one has to compactificate now three dimensions, and not one. And of course the question occurs: why the spacetime initial dimension is equal to 11? And why 7 of them should compactify later? Why all of the compactified dimensions are spatial ones? Typical explanations given in literature look like the following one. The simplest answer on this question can consist in that because of special features of theories under consideration compactification can result only in 4dimensional space. In the frames of inflationary Universe scenario there exists one more opportunity of answering the question. Indeed, let us suppose that compactification can result not only in 4dimensional space but in the spaces of any dimensions. It is clear that, in causallydisconnected regions of the Universe, compactification processes were independent of each other and therefore dimensions of the different regions of the Universe could be different... If during (or after) the compactification the inflation of the Universe took place, after the inflation our Universe appear to be divided on many miniuniverses of different dimensions including that of dimension 4.We have to notice now that the conditions necessary for life existence (existence of planets, atoms, etc.) can take place only in fourdimensional spacetime. Indeed, even Ehrenfest noted (see 54,70 for further details) that in spaces with dimensions high than 4 gravitational and electromagnetic attractions decrease with distance too fast to admit the formation of bounded states like atoms or planets. On the other hand, according to general relativity, in spaces with dimensions less than 4 attraction does not exist at all. Hence we live in 4dimensional islands of the Universe. Their dimensions make our existence possible (26,55) (Linde,1984,p.202).
I think that such an argument can have farreaching consequences. Why each of us has two hands?  Because if he had one hand he could not survive in the natural selection process and could not answer the question. Why all the bodies fall on the surface of the Earth?  Since if they fly away, the man who asked the question was away also. And so on. Of course dimension is not a single parameter necessary for life genesis and for occurence of Reason. To my mind the number of such parameters is infinite that corresponds to infinite number of 4dimensional universes with different values of the fundamental constants. Let us have infinite number of the universes with various dimensions and one with dimension 4.But to have such an object is not enough to have life on it. There are other parameters  electron charge, for instance. So, we should have infinite number of the universes with different magnitudes of electron charge, where one exists with the magnitude of our own. Still we want infinite universes with different electron mass magnitudes, and so on. Hence the probability to find oneself in the Universe with our collection of fundamental constants is practically zero.
Hence the dimensionality problem is not solved by an anthropic argument. It is merely reformulated to create an illusion of the answer.
Moreover. We have additional scalar fields connected with 4+D metric components. What shall we do with them now? Where can one find so many Branses and Dickes to look for their places in the Universe?
And some new problems occur that were absent in the genuine KaluzaKlein theory. The first one is the problem of vacuum stability and the second one consists in that the 4 x D manifold is not a solution of the Einstein equations in vacuum. It is a serious drawback that spoils the picture significantly. One can conclude that the main KaluzaKlein shortcoming  the lack of new content in comparison with the older theories  remains in the generalized multidimensional versions of the original 5dimensional theory. The unified case contains the same information as the number of theories before unification. Nothing new. The origin of the drawback consists in the following. Multidimensional generalization of the KaluzaKlein theory is as trivial as the 5dimensional original version since
it represents simple translation of the gauge invariance idea into the geometrical language. It is clear that it contains nothing new in comparison to the YangMills equations just as the translation of Conan Doyles story from English into German cannot transmute the detective Sherlock Holmes into the criminal professor Moriarty and vice versa. Thus all the recent advances in physics considered appear to have mainly mathematical significance. The mathematicians found the means of translating the apparatus of the theory from one mathematical language to another. From PASCAL to FORTRAN. From algebra to geometry and vica versa. But what about physics? Can all these fuss have anything to do with physics? With real experiments? Can the theory describe the results of even gedankenexperiments? Has it any physical significance? To my mind, to explain the successes of the superstring theories one arrives at sociological scenario. Not Karl Popper &Imre Lakatos, but David Bloor &Andrew Pickering are useful. In his Constructing Quarks the Edinburgh thinker had proposed a framework for understanding the dynamics of practice called the model of opportunism in context. The archetype of the model are two research traditions, one experimental and the other theoretical, devoted to exploration and explanation of the same natural phenomenon. The point is that all the two traditions need each other to flourish. Consider the theoretical tradition. To justify his choice to work within certain theoretical tradition, a theorist should cite the experimental data in need of explanation. On the other hand, experimenters decision to investigate the phenomena in question is justified by its theoretical significance. Thus, theoretical and experimental traditions constitute mutually reinforcing contexts. The same is true for the cases when the traditions at issue are purely theoretical ones. Each scientist has at his disposal a set of resources for constructive research. The experimenter, for instance, may have access to a particular apparatus. The theoretician can have expertise in particular branches of experiment or theory acquired in the course of professional career. All these resources may be well or ill matched to particular contexts. Different research strategies may have different relative opportunities presented by different contexts for the constructive exploitation of the resources available to individual scientists. Now let me turn to superstrings. Their proliferation was caused by a great amount of mathematical physicists or simply mathematicians who had special skills for treating the general relativistic problems. And the SUSY theories provided the context to use the skills theoreticians were specially trained for. As far as I know, the majority of superenthusiasts came from pure geometry. Their dreams of finding the laws of Nature by simple transformations from one system of reference to another had many chances to be realized. Moreover, the superstring vocabulary provides the means for pure mathematicians to use physical notions and, in particular, to publish in Communications in the Mathematical Physics, The Physical Review D and to get grants on future research from physical foundations. After black holes , white holes, naked and dressed singularities were scrutinized, the army of mathematicians was looking for other jobs. And they found the new wonderful domain  the Supergravity. The ocean of Mathematical Speculation admits a plenty of mathematical crews to swim. SUSY contains too many new terms to play with and to accomodate to the wellknown experimental data that will unavoidably lead to new discoveries in the Brave New World of Superstrings. REFERENCES.
Chyba C.F.(1985) : KaluzaKlein unified field theory and apparent four  dimensional spacetime. American Journal of Physics, 53(9),pp.863872.
Dokshitzer Yu.L.,Dyakonov D.I.,Troyan S.I.(1979) : Hard Processes in Quantum Chromodynamics. Physics Reports,vol.58,pp.269395.
Hey A.J.G.(1979) : Particle Systematics. Elementary Particles Studies, pp.523546.
Linde A.D.(1984) : Inflating Universe. Soviet Physics: Uspekhi, vol.111,2, p.202 (in Russian).
Nugayev R.M. (1987) : The genesis and structure of models in the modern theory of gravity. International Studies in the Philosophy of Science, vol.2, number1,pp.84104.
Nugayev R.M. (1996) : Why did the new physics force out the old? International Studies in the Philosophy of Science,vol.10,no 2,pp.127 140.
Pickering A.(1985) : Constructing Quarks. A Sociological History of Particle Physics. The University of Chicago Press.
Stepin V.S.(1976) : The Formation of a Scientific Theory. Minsk, Belorussian University Press (in Russian).
Vladimirov Yu. V.(1989) : Spacetime: explicit and implicit dimensions. Moscow, Nauka (in Russian).
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