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Table of contents
1 Strings, fields and branes
1.1 Supersymmetric relativistic strings
1.2 Type II supergravities
1.3 Supergravity in D=
1.4 Supersymmetric vacuum solutions
1.5 D-branes
1.6 The AdS/CFT Correspondence
2 Mass deformations of N = 4 SYM and their supergravity duals
2.1 Myers effect
2.2 The N = 1? theory
2.3 Moving towards the N = 0? theory
2.4 Group theory for generic mass deformations
2.4.1 Fermionic masses
2.4.2 Bosonic Masses
2.5 The explicit map between bosonic and fermionic mass matrices
2.6 Mass deformations from supergravity
2.7 The trace of the bosonic and fermionic mass matrices
2.7.1 Constraints on the gauge theory from AdS/CFT
2.7.2 Quantum corrections in the gauge theory
3 Supersymmetry and (Generalized) Geometry
3.1 Supersymmetry, topology and geometry
3.2 O(d,d) Generalized Geometry
3.2.1 Geometrizing the NS-NS degrees of freedom
3.2.2 Supersymmetry in O(d,d) Generalized Geometry
3.3 Exceptional Generalized Geometry
4 Generalized Geometric vacua with eight supercharges
4.1 Supersymmetry in Exceptional Generlaized Geometry
4.1.1 Backgrounds with eight supercharges
4.1.2 Supersymmetry conditions
4.2 From Killing spinor equations to Exceptional Sasaki Einstein conditions
4.2.1 The Reeb vector
4.2.2 The H and V structures as bispinors
4.2.3 Proof of the generalized integrability conditions
4.3 The M-theory analogue
4.4 Some constraints from supersymmetry
4.4.1 Type IIB
4.4.2 M-theory
4.5 The moment map for Ja
4.5.1 Type IIB
4.5.2 M-theory
4.6 The Dorfman derivative along K
4.6.1 Type IIB
4.6.2 M-theory
A ’t Hooft symbols
B Spinor conventions
C E6 representation theory
C.1 SL(6) × SL(2) decomposition
C.2 USp(8) decomposition
C.3 Transformation between SL(6) × SL(2) and USp(8)
