N = 2 supergravity in d = 4, 5, 6 and its matter couplings

Van Proeyen A.

Table of contents :
Introduction……Page 5
Overview of supersymmetric theories with 8 real supercharges……Page 7
Multiplets…….Page 8
The strategy……Page 10
Rigid conformal symmetry……Page 11
Superconformal groups……Page 17
Rules of (super)gauge theories, gauge fields and curvatures…….Page 20
Gauging spacetime symmetries and the Weyl multiplet…….Page 21
Transformations of the vielbeins……Page 22
Transformations of the other gauge fields……Page 23
Covariant quantities and covariant derivatives……Page 25
Proof of theorem on covariant derivatives……Page 26
Example of d=6 vector multiplet……Page 27
Illustration of full calculation of the transformation of a curvature……Page 28
The easy way……Page 29
Consequences of the constraint on R(P)……Page 31
Other constraints……Page 33
Conformal invariant actions……Page 34
Matter fields completing the Weyl multiplet……Page 36
d=4……Page 40
d=5……Page 42
d=6……Page 43
Example in bosonic case……Page 44
Conformal properties of the multiplets…….Page 45
Vector multiplets……Page 46
Chiral multiplet……Page 49
Hypermultiplets……Page 52
Tensor multiplet in d=4……Page 59
Vector multiplets in 4 dimensions……Page 60
Hypermultiplets……Page 64
Gauge fixing of superconformal symmetries……Page 68
Projective Kähler geometry……Page 69
Interpretation as Sasakian cone……Page 74
The resulting bosonic action and examples……Page 75
Hypermultiplet action……Page 78
The gauge fixing of the total action……Page 80
Equations of motion……Page 81
Gauge choices and decomposition laws……Page 82
Dualities in general…….Page 83
Symplectic transformations in N=2……Page 86
Symplectic formulation……Page 88
Absence of a prepotential in examples……Page 90
Definitions……Page 92
Symplectic equations and the curvature tensor……Page 93
A mathematically inspired definition……Page 96
The spacetime ansatz and an effective action……Page 100
Maxwell equations and the black hole potential……Page 102
Field strengths and charges……Page 104
Gauge transformations as isometries……Page 106
Realizations in Calabi–Yau moduli spaces…….Page 109
Action and main transformation laws from general considerations……Page 110
Vector multiplet and algebra……Page 111
Algebra and gravitino transformation……Page 112
Determining the shifts……Page 113
Very special real and quaternionic-Kähler manifolds……Page 115
Quaternionic-Kähler manifolds……Page 116
The family of special manifolds……Page 117
Old on c-map……Page 119
Homogeneous and symmetric spaces…….Page 120
5 dimensions……Page 123
4 dimensions……Page 127
Further developments……Page 131
Bosonic part……Page 132
d=4……Page 135
d=5……Page 138
Gamma matrix manipulations……Page 140
Spinor indices……Page 141
Products of matrices and Fierzing……Page 143
Groups and supergroups……Page 145
Other N=2, d=4 papers……Page 148
Translations from/to form language……Page 150
Identities of very special geometry……Page 151
Rigid supersymmetry……Page 153