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