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| 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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