Noncommutative Supersymmetric/Integrable Models and String Theory

Introduction......Page 3 The Moyal product......Page 13 The natural Moyal deformation of a field theory......Page 20 Other possible deformations: The free scalar field theory example......Page 26 The Kontsevich product......Page 28 Deforming superspace......Page 30 Non(anti)commutative superspace......Page 33 N=12 supersymmetry......Page 43 Noncommutative Yang-Mills theory from the open string......Page 47 Generalization to the superstring in RNS and GS formalisms......Page 55 Noncommutative selfdual Yang-Mills from the N=2 string......Page 58 Non(anti)commutative field theories from the covariant superstring......Page 60 Generalization to non-constant backgrounds......Page 66 Infinite conserved currents and the bicomplex approach......Page 69 Reductions from selfdual Yang-Mills......Page 72 Properties of the S-matrix......Page 74 Solitons......Page 75 Noncommutative solitons......Page 76 Noncommutative deformation of integrable field theories......Page 79 The natural noncommutative generalization of the sine-Gordon model......Page 80 A noncommutative version of the sine-Gordon equation with an infinite number of conserved currents......Page 81 Reduction from noncommutative selfdual Yang-Mills......Page 83 The action......Page 85 The relation to the noncommutative Thirring model......Page 86 (Bad) properties of the S-matrix......Page 87 Conclusions......Page 90 Introduction......Page 92 A noncommutative integrable sigma model in 2+1 dimensions......Page 93 Reduction to noncommutative sine-Gordon......Page 96 Relation with the previous noncommutative generalization of the sine-Gordon model......Page 100 Solitons......Page 102 (Nice) properties of the S-matrix......Page 108 Conclusions......Page 116 Motivation: Problems with RNS and GS formalisms......Page 117 Pure spinor superstring basics......Page 119 Type II superstring vertex operators......Page 124 Amplitudes......Page 127 What we can (cannot) do with this formalism, up to now......Page 129 Warm up: The open superstring case......Page 132 Linearized IIA/IIB supergravity equations......Page 134 Gauge transformations and gauge fixing......Page 137 Recursive equations and explicit solution (up to order 22)......Page 140 Gauge fixing for massive states......Page 143 The ansatz for the RR field strength......Page 147 The vertex for linearly x-dependent RR field strength......Page 149 Vertex operators with R-R gauge potentials......Page 150 Antifields and the kinetic terms for closed superstring field theory......Page 151 Conclusions and outlook......Page 153 Superspace conventions in d=4......Page 161 Superspace conventions in d=10......Page 164 Acknowledgements......Page 165