超對稱和超引力導(dǎo)論

前言

This book has evolved out of a number of courses that I have given on supersymmetry and supergravity．While giving these lectures I became convinced of the need for a book which contained a pedagogical introduction to most aspects of supersymmetric theories．Although the content of this book has been to some extent constrained by those areas that were my research activities at the time 1 wrote my lecture notes，most major areas relevant for an Introduction are covered，as well as some more advanced topics．Some of the latter are concerned with the quantum properties of supersymmetric  theories and the construction of supergravity theories．The final chapter contains a discussion of free gauge covariant string field theory．Supersymmetric theories have had an important influence on the theoretical physics community．It has encouraged the quest for a single unified theory of physics and has lead to a wider understanding of what can constitute the space-time we live in．On a more generaIlevel．it has made more acceptable the study of ideas which are at first sight rather distantly related to experi． mental data．Some effort has been made to present a stepby．step and necessarily technical derivation of the results．However．by studying the subject itself, it iS hoped that the reader will also come to appreciate more fully the concepts that may be abstracted from supersymmetric theories． I would like to express my gratitude to King's College，the California Institute of Technology and CERN where this manuscript was written and typed．I also wish to thank my collaborators for the insights they have shared with me．

內(nèi)容概要

The first edition of this book was completed in 1986, however, much of the material was written long before. It focused on the development of fourdimensional supersymmetric models including supergravity with emphasis on their ultraviolet properties. Already in 1983, our understanding of the finiteness of rigid supersymmetric theories had led to the realization that supersymmetry was most unlikely to solve the celebrated inconsistency of quantum mechanics and gravity. This, and the fact that many aspects Of supersymmetric theories had been worked out, lead to a search for new ideas. It was inevitable that string theory, which had been extensively developed in the late 1960's and early 1970's would be revived from its dormant state. We recall that supersymmetry was discovered independently in two ways, one of which was within the superstring which contained it as a symmetry. Also during the dormant stage, theoreticians had developed BRST symmetry, conformal models, the vertex operator representation of Liealgebras, the use of the gauge group Es for grand unified models, even within the context of ten-dimensional supersymmetric theories and gained further understanding of anomalies. All these enabled the solution of some of the problems which the original pioneers of string theory had encountered.

作者簡介

作者：（英國）韋斯特（Peter West）

書籍目錄

preface to the second edition preface 1. introduction 2. the supersymmetry algebra 3. alternative approaches to the supersymmetry algebra 4. immediate consequences of the supersymmetry algebra 5. the wess-zumino model 6. n = 1 supersymmetric gauge theory: super qed 7. n = 1 yang-mills theory and the noether technique 8. the irreducible representations of supersymmetry 9. simple supergravity: linearized n = 1 supergravity 10. invariance of simple supergravity 11. tensor calculus of rigid supersymmetry 11.1 supermultiplets 11.2 combination of supermultiplets 11.3 action formulas 12. theories of extended rigid supersymmetry 12.1 n = 2 yang-mills 12.2 n = 2 matter 12.3 the general n = 2 rigid theory 12.4 the n = 4 yang-mills theory 13. the local tensor calculus and the coupling of supergravity to matter 14. superspace 14.1 an elementary account of n = 1 superspace 14.2 n = 1 superspace 14.3. n = 2 superspace 15. superspace formulations of rigid supersymmetric theories 15.1 n = 1 superspace theories: the wess-zumino model 15.2 n = 1 yang-mills theory 15.3 a geometrical approach to n = 1 supersymmetric yang-mills theory 15.4 n = 2 superspace theories 16. superspace formulation of n = 1 supergravity 16.1 geometry 16.2 the superspace constraints 16.3 analysis of the superspace constraints 16.4 superspace supergravity. from x-space supergravity 17. n = 1 super-feynman rules 17.1 general formalism 17.2 the wess-zumino multiplet 17.3 super yang-mills theory 17.4 applications of n = 1 super-feynman rules 17.5 divergence in super-feynman graphs 17.6 one-loop infinities in a general n = 1 supersymmetric theory 17.7 the background-field method 17.8 the superspace background-field method 18. ultra-violet properties of the extended rigid supersymmetric theories 18.1 the anomalies argument 18.2 the non-renormalization argument 18.3 finite n = 2 supersymmetric rigid theories 18.4 explicit breaking and finiteness 19. spontaneous breaking of supersymmetry and realistic models 19.1 tree-level breaking of supersymmetry 19.2 quantum breaking of supersymmetry 19.3 the gauge hierarchy problem 19.4 comments on the construction of realistic models 20. currents in supersymmetric theories 20.1 general considerations 20.2 currents in the wess-zumino model 20.3 currents in n = i super yang-mills theory 20.4 quantum generated anomalies 20.5 currents and supergravity formulations 21. introduction to two-dimensional supersymmetric models and superstring actions 21.1 2-dimensional models of rigid supersymmetry 21.2 coupling of 2-dimensional matter to supergravity 22. two-dimensional supersymmetry algebras 22.1 conventions in two-dimensional minkowski and euclidean spaces 22.2 superalgebras in two-dimensions 22.3 irreducible representations of two-dimensional supersymmetry 23. two-dimensional superspace and the construction of models 23.1 minkowski superspaces 23.2 euclidean superspaces 24. superspace formulations of two-dimensional supergravities 24.1 geometrical framework 24.2 (1,0) supergravity 24.3 (1, 1) supergravity 25. the superconformal group 25.1 the conformal group in arbitrary dimensions 25.2 the two-dimensional conformal group 25.3 the (1, 1) superconformal group 25.4 the (2, 2) superconformal group 26. green functions and operator product expansions in (2, 2) superconformal models 26.1 two and three point green functions 26.2 chiral correlators in (2, 2) superconformal models 26.3 super operator product expansions 27. gauge covariant formulation of strings 27.1 the point particle 27.2 the bosonic string 27.3 oscillator formalism 27.4 the gauge covariant theory at low levels 27.5 the finite set 27.6 the infinite set 27.7 the master set 27.8 the on-shell spectrum of the master set appendix a: an explanation of our choice of conventions appendix b: list of reviews and books appendix c: problems references subject index

章節(jié)摘錄

插圖：Supersymmetry was discovered by Golfand and Liktman.A theory invar .ant under a non。linear realization of supersymmetry was giyen by Akulov and Volkov.In a separate development，supersymmetry was introduced as a two-dimensional symmetry of the world sheet within the context of string theories·However，supersymmetry only became widely known when this two-dimensional symmetry was generalized to four dimensions and used to construct the Wess-Zumino model.  To this day，there is no firm evidence that supersymmetry is realized in Nature.Neither is there any completely compelling reason to believe that supersymmetry is required to resolve any of the paradoxes of our present theories of physics.However，it is possible that supersymmetry may be re.qmred to explain the new phenomena found already，or in the near future.in particle accelerators.On the theoretical side，there are also some reasonsto hOpe that supersymmetry is required.In Nature。there are at least two vastly different energy scales：the weak scale（100 GeV）and the Planck scale（10GeV）.There are also some reasons to believe that there should be one or more Intermediate scales.Although the origin of these vastly different scalesis unknown，it is considered to be natural to have a theory in which phenome.na at the lowest scale are not polluted by much larger effects arising fromthe higher scales.Some supersymmetric theories are natural in this sense.andit is a consequence of this argument that the superpartners of the observed particles ought to have masses around the weak scale and hence should be seen in the near future（see Chapter 1 9）.This particular property of super.symmetric theories IS a consequence of the fact that the spin.zero states are related by supersymmetry to states of spin.   The most uncertain aspect of the standard model of weak and electromag.netlc interactions is the spin-zero sector.In fact，many ofthe 19 free parameters of this model arise due to the undetermined interactions of the spin.zero fields with themselves and the spin-fields.It is natural to hope that some of theselree parameters are fixed in a supersymmetric theory.In fact，this has not been achmved within the context of supersymmetric models with onlY one super.symmetry，but 1t is likely to be the case should one succeed in constructing a realistic model with more than one supersymmetry.

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