Index theory and dynamical symmetry enhancement near IIB horizons

Abstract

We show that the number of supersymmetries of IIB black hole horizons is N = 2N- + 2 index(Dλ), where index(D λ) is the index of the Dirac operator twisted with the line bundle λ1/2 of IIB scalars, and N- is the dimension of the kernel of a horizon Dirac operator which depends on IIB fluxes. Therefore, all IIB horizons preserve an even number of supersymmetries. In addition if the horizons have non-trivial fluxes and N- ≠ 0, then index(Dλ) ≥ 0 and the horizons admit an sl(2, ℝ) symmetry subalgebra. This provides evidence that all such horizons have an AdS/CFT dual. Furthermore if the orbits of sl(2, ℝ) are two-dimensional, the IIB horizons are warped products AdS2 xw S. © SISSA 2013.