Recent years have brought a revival of work on string theory, which has been a source of fascination since its origins nearly twenty years ago.There seems to be a widely perceived need for a systematic, pedagogical exposition of the present state of knowledge about string theory. We hope that this book will help to meet this need. To give a comprehensive account of such a vast topic as string theory would scarcely be possible,even in two volumes with the length to which these have grown. Indeed,we have had to omit many important subjects, while treating others only sketchily. String field theory is omitted entirely (though the subject of chapter 11 is closely related to light-cone string field theory). Conformal field theory is not developed systematically, though much of the background material needed to understand recent papers on this subject is presented in chapter 3 and elsewhere.
Preface
8 One-loop diagrams in the bosonic string theory
8.1 Open-string one-loop amplitudes
8.1.1 The planar diagrams
8.1.2 The nonorientable diagrams
8.1.3 Nonplanar loop diagrams
8.2 Closed-string one-loop amplitudes
8.2.1 The torus
8.2.2 Modular invariance
8.2.3 The integration region
8.2.4 Analysis of divergences
8.2.5 The cosmological constant
8.2.6 Amplitudes with closed-string massless states
8.3 Other diagrams for unoriented strings
8.3.1 Higher-order tree diagrams
8.3.2 The real projective plane
8.3.3 Other loop diagrams
8.4 Summary
8.A Jacobi 0 functions
9 One-laop diagrams in superstring theory
9.1O pemsuperstring amplitudes
9.1.1 Amplitudes with M 4 massless external states
9.1.2 The planar diagrams
9.1.3 Nonorientable diagrams
9.1.4 Orientable nonplanar diagrams
9.2 Type II theories
9.2.1 a Finiteness of the torus amplitude
9.2.2 Compactification on a torus
9.2.3 The low-energy limit of one-loop amplitudes
9.3 The hea;erotic string theory
9.3.1 The torus with four external particles
9.3.2 Modular invariance of the Es a Es and SO(32) theories
9.4 Calculations in the RNS formalism
9.4.1 Modular invariance and the GSO projection
9.4.2 The loop calculations
9.5 Orbifolds and twisted strings
9.5.1 Generalization of the GSO projection
9.5.2 Strings on orbifolds
9.5.3 Twisted strings in ten dimensions
9.5.4 Alternative view of the SO(16) a SO(16) theory
9.6 Summary
9.A Traces of fermionic zero modes
9.B Modular invariance of the functions F2 and/:
10 The gauge anomaly in type I superstring theory
10.1 Introduction to anomalies
10.1.1 Anomalies in point-particle field theory
10.1.2 The gauge anomaly in D = 10 super Yang-Mills theory
10.1.3 Anomalies in superstring theory
10.2 Analysis of hexagon diagrams
10.2.1 The planar diagram anomaly
10.2.2 The anomaly in the nonorientable diagram
10.2.3 Absence of anomalies in nonplanar diagrams
10.3 Other one-loop anomalies in superstring theory
10.4 Cancellation of divergences for SO(32)
10.4.1 Dilaton tadpoles and loop divergences
10.4.2 Divergence cancellations
10.5 Summary
10.A An alternative regulator
11 Functional methods in the light-cone gauge
11.1 The string path integral
11.1.1 The analog model
11.1.2 The free string propagator
11.1.3 A lattice cutoff
11.1.4 The continuum limit
11.2 Amplitude calculations
11.2.1 Interaction vertices
11.2.2 Parametrization of scattering processes
11.2.3 Evaluation of the functional integral
11.2.4 Amplitudes with external ground statm
11.3 Open-string tree amplitudes
11.3.1 The conformal mapping
11.3.2 Evaluation of amplitudes
……
12 Some differential geometry
13 Low-energy effective action
14 Compactiflcation of higher dimensions
15 Some algebraic geometry
16 Models of low-energy supersymmetry
Bibliography
Index
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