# (26.11.) Generalising Calabi-Yau for generic flux backgrounds

Anthony Ashmore (Imperial)

26.11.2015 at 16:15

Calabi-Yau manifolds without flux are perhaps the best-known supergravity backgrounds that leave some supersymmetry unbroken. The supersymmetry conditions on such spaces can be rephrased as the existence and integrability of a particular geometric structure. When fluxes are allowed, the conditions are more complicated and the analogue of the geometric structure is not well understood. In this talk, I will define the analogue of Calabi-Yau geometry for generic D=4, N=2 backgrounds with flux in both type II and eleven- dimensional supergravity. The geometry is characterised by a pair of G-structures in 'exceptional generalised geometry' that interpolate between complex, symplectic and hyper-Kahler geometry. Supersymmetry is then equivalent to integrability of the structures, which appears as moment maps for diffeomorphisms and gauge transformations. Similar structures also appear in D=5 and D=6 backgrounds with eight supercharges. As a simple application, I will discuss the case of AdS5 backgrounds in type IIB, where deformations of these geometric structures give exactly marginal deformations of the dual field theories.

Arnold Sommerfeld Center

Theresienstrasse 37

Room 348