超弦和M理論導(dǎo)論

前言

Superstring theory (and its latest formulation, M-theory) has emerged as the most promising candidate for a quantum theory of all known interactions. Superstrings apparently solve a problem that has defied solution for the past50 years, namely the unification of the two great fundamental physical theories of the century, quantum field theory and general relativity. Superstring theory introduces an entirely new physical picture into theoretical physics and a new mathematics that has startled even the mathematicians. Ironically, although superstring theory is supposed to provide a unified field theory of the Universe, the theory itself often seems like a confused jumble of folklore, random rules of thumb, and intuitions. This is because the development of superstring theory has been unlike that of any other theory, such as general relativity, which began with a geometry and an action and later evolved into a quantum theory. Superstring theory, by contrast, has been evolving backward for the past 30 years. It has a bizarre history, beginning with the purely accidental discovery of the quantum theory in 1968 by G. Veneziano and M. Suzuki. Thumbing through old mathematics books, they stumbled by chance on the Beta function, written down in the last century by mathematician Leon hard Euler. To their amazement, they discovered that the Beta function satisfied almost all the stringent requirements of the scattering matrix describing particle interactions. Never in the history of physics has an important scientific discovery been made in quite this random fashion.

內(nèi)容概要

　超弦和M理論是現(xiàn)代物理學(xué)中最有趣最活躍的研究課題之一。該問題比較困難同時(shí)也充滿爭(zhēng)議，一些人稱之為“終極理論”，這是因?yàn)槌依碚撚锌赡芙鉀Q困擾人們多年的難題，即統(tǒng)一二十世紀(jì)最偉大的兩個(gè)理論：廣義相對(duì)論和量子場(chǎng)論。本書全面細(xì)致地講解超弦理論和該領(lǐng)域的最新研究進(jìn)展，內(nèi)容包括四維超弦，Kac-Moody代數(shù)，Teichmuller空間和Calabi-Yau流形，M理論和D膜，對(duì)偶和BPS關(guān)系，矩陣模型等，可以作為研究生教材，同時(shí)對(duì)研究人員也有參考價(jià)值。作者首先簡(jiǎn)要介紹了點(diǎn)粒子理論，然后利用費(fèi)曼路徑積分詳細(xì)討論超弦理論。超弦研究需要很多數(shù)學(xué)工具，書中分別作了介紹，如指標(biāo)定理，同調(diào)論和Kahler流形等。在第二版中，作者對(duì)內(nèi)容做了整體修訂，并添加了M理論的三個(gè)新章節(jié)。閱讀本書需要量子力學(xué)和相對(duì)論的基本知識(shí)?！　∽x者對(duì)象：理論物理、高能物理、場(chǎng)論和弦論等專業(yè)的高年級(jí)本科生、研究生和相關(guān)專業(yè)的科研人員。

作者簡(jiǎn)介

作者：（美國(guó)）加來(lái)道雄

書籍目錄

Preface Acknowledgments Ⅰ First Quantization and Path Integrals 1 Path Integrals and Point Particles 1.1 Why Strings? 1.2 Historical Review of Gauge Theory 1.3 Path Integrals and Point Particles 1.4 Relativistic Point Particles 1.5 First and Second Quantization 1.6 Faddeev-Popov Quantization 1.7 Second Quantization 1.8 Harmonic Oscillators 1.9 Currents and Second Quantization 1.10 Summary References 2 Nambu-Goto Strings 2.1 Bosonic Strings 2.2 Gupta-Bleuler Quantization 2.3 Light Cone Quantization 2.4 BRST Quantization 2.5 Trees 2.6 From Path Integrals to Operators 2.7 Projective Invariance and Twists 2.8 Closed Strings 2.9 Ghost Elimination 2.100 Summary References 3 Superstrings 3.1 Supersymmetric Point Particles 3.2 Two-Dimensional Supersymmetry 3.3 Trees 3.4 Local Two-Dimensional Supersymmetry 3.5 Quantization 3.6 GSO Projection 3.7 Superstrings 3.8 Light Cone Quantization of the GS Action 3.9 Vertices and Trees 3.10 Summary References 4 Conformal Field Theory and Kac——Moody Algebras 4.1 Conformal Field Theory 4.2 Superconformal Field Theory 4.3 Spin Fields 4.4 Superconformal Ghosts 4.5 Fermion Vertex 4.6 Spinors and Trees 4.7 Kac-Moody Algebras 4.8 Supersymmetry 4.9 Summary References 5 Mulfiloops and Teichmuller Spaces 5.1 Unitarity 5.2 Single-Loop Amplitude 5.3 Harmonic Oscillators 5.4 Single-Loop Superstring Amplitudes 5.5 Closed Loops 5.6 Multiloop Amplitudes 5.7 Riemann Surfaces and Teichmiiller Spaces 5.8 Conformal Anomaly 5.9 Superstrings 5.10 Determinants and Singularities 5.11 Moduli Space and Grassmannians 5.12 Summary References Ⅱ Second Quantization and the Search for Geometry 6 Light Cone Field Theory 6.1 Why String Field Theory? 6.2 Deriving Point Particle Field Theory 6.3 Light Cone Field Theory 6.4 Interactions 6.5 Neumann Function Method 6.6 Equivalence of the Scattering Amplitudes 6.7 Four-String Interaction 6.8 Superstring Field Theory 6.9 Summary References 7 BRST Field Theory 7.1 Covariant String Field Theory 7.2 BRST Field Theory 7.3 Gauge Fixing 7.4 Interactions 7.5 Witten's String Field Theory 7.6 Proof of Equivalence 7.7 Closed Strings and Superstrings 7.8 Summary References Ⅲ Phenomenology and Model Building 8 Anomalies and the Atiyah-Singer Theorem 8.1 Beyond GUT Phenomenology 8.2 Anomalies and Feynman Diagrams 8.3 Anomalies in the Functional Formalism 8.4 Anomalies and Characteristic Classes 8.5 Dirac Index 8.6 Gravitational and Gauge Anomalies 8.7 Anomaly Cancellation in Strings 8.8 Summary References 9 Heterotic Strings and Compactification 9.1 Compactification 9.2 The Heterotic String 9.3 Spectrum 9.4 Covariant and Fermionic Formulations 9.5 Trees 9.6 Single-Loop Amplitude 9.7 Es and Kac——Moody Algebras 9.8 Lorentzian Lattices 9.9 Summary References 10 Calabi——Yau Spaces and Orbifolds 10.1 Calabi-Yau Spaces 10.2 Review of de Rahm Cohomology 10.3 Cohomology and Homology 10.4 K/ihler Manifolds 10.5 Embedding the Spin Connection 10.6 Fermion Generations 10.7 Wilson Lines 10.8 Orbifoids 10.9 Four-Dimensional Superstrings 10.10 Summary References Ⅳ M-Theory 11 M-Theory and Duality 11.1 Introduction 11.2 Duality in Physics 11.3 Why Five String Theories? 11.4 T-Duality 11.5 S-Duality 11.5.1 Type IIA Theory 11.5.2 Type IIB Theory 11.5.3 M-Theory and Type IIB Theory 11.5.4 E8 E8 Heterotic String 11.5.5 Type I Strings 11.6 Summary References 12 Compactifications and BPS States 12.1 BPS States 12.2 Supersymmetry and P-Branes 12.3 Compactification 12.4 Example: D = 6 12.4.1 D = 6, N = (2, 2) Theory 12.4.2 D = 6, N = (1, 1) Theories 12.4.3 M-Theory in D = 7 12.5 Example:D=4, N=2 and D=6, N=1 12.6 Symmetry Enhancement and Tensionless Strings 12.7 F-Theory 12.8 Example: D = 4 12.9 Summary References 13 Solitons, D-Branes, and Black Holes 13.1 Solitons 13.2 Supermembrane Actions 13.3 Five-Brahe Action 13.4 D-Branes 13.5 D-Brane Actions 13.6 M(atrix) Models and Membranes 13.7 Black Holes 13.8 Summary 13.9 Conclusion References Appendix A.1 A Brief Introduction to Group Theory A.2 A Brief Introduction to General Relativity A.3 A Brief Introduction to the Theory of Forms A.4 A Brief Introduction to Supersymmetry A.5 A Brief Introduction to Supergravity A.6 Notation References Index

章節(jié)摘錄

插圖：(1) Because we are dealing with a first quantized theory, we have to take the sum over all interacting topologies that are swept out by the string. For the Nambu——Goto string, the precise nature of these topologies is ambiguous and must be specified by hand. However, for the Polyakov form of the action, which contains an independent metric tensor, we can eliminate most of this ambiguity by specifying that we sum over all conformally and modular in equivalent configurations. (These terms will be defined later.) This will become a powerful constraint once we start to derive loops and will determine the function measure uniquely. The measure and the topologies in the Nambu-Goto action, however, are not well defined.  (We must point out, however, that this rule of integrating over in equivalent surfaces does not automatically satisfy unitarity. This still must be checked by hand.)(2) The gauge fixing of weyl invariance for the Polyakov action, although trivial classically, poses problems when we make the transition to quantum mechanics. An anomaly appears when we carefully begin the quantization process. In fact, this conformal anomaly will disappear only in 26dimensions.

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