Gravity and Strings

x Contents
3.1.1 Scalar gravity coupled to matter 47
3.1.2 The action for a relativistic massive point-particle 48
3.1.3 The massive point-particle coupled to scalar gravity 50
3.1.4 The action for a massless point-particle 51
3.1.5 The massless point-particle coupled to scalar gravity 53
3.1.6 Self-coupled scalar gravity 53
3.1.7 The geometrical Einstein–Fokker theory 55
3.2 Gravity as a self-consistent massless spin-2 SRFT 57
3.2.1 Gauge invariance, gauge identities, and charge conservation
in the SRFT of a spin-1 particle 60
3.2.2 Gauge invariance, gauge identities, and charge conservation
in the SRFT of a spin-2 particle 63
3.2.3 Coupling to matter 67
3.2.4 The consistency problem 76
3.2.5 The Noether method for gravity 78
3.2.6 Properties of the gravitational energy–momentum tensor t (0)
GR µσ 85
3.2.7 Deser’s argument 89
3.3 General relativity 96
3.4 The Fierz–Pauli theory in a curved background 103
3.4.1 Linearized gravity 104
3.4.2 Massless spin-2 particles in curved backgrounds 108
3.4.3 Self-consistency 112
3.5 Final comments 112
4 Action principles for gravity 114
4.1 The Einstein–Hilbert action 115
4.1.1 Equations of motion 117
4.1.2 Gauge identity and Noether current 119
4.1.3 Coupling to matter 120
4.2 The Einstein–Hilbert action in different conformal frames 121
4.3 The first-order (Palatini) formalism 123
4.3.1 The purely affine theory 126
4.4 The Cartan–Sciama–Kibble theory 127
4.4.1 The coupling of gravity to fermions 128
4.4.2 The coupling to torsion: the CSK theory 131
4.4.3 Gauge identities and Noether currents 134
4.4.4 The first-order Vielbein formalism 136
4.5 Gravity as a gauge theory 140
4.6 Teleparallelism 144
4.6.1 The linearized limit 146
5 N = 1, 2, d = 4 supergravities 150
5.1 Gauging N = 1, d = 4superalgebras 151
5.2 N = 1, d = 4 (Poincaré) supergravity 155
5.2.1 Local supersymmetry algebra 158