Index theory and dynamical symmetry enhancement near IIB horizons

TL;DR

This paper analyzes the supersymmetry properties of IIB black hole horizons, revealing conditions under which they preserve even supersymmetries and exhibit enhanced symmetries related to AdS/CFT correspondence.

Contribution

It establishes a formula relating supersymmetry count to the index of a twisted Dirac operator and shows conditions for symmetry enhancement and AdS/CFT duality in IIB horizons.

Findings

All IIB horizons preserve an even number of supersymmetries.

Non-trivial fluxes and non-zero N_- imply an sl(2,R) symmetry.

Horizons with 2D sl(2,R) orbits are warped AdS_2 x S geometries.

Abstract

We show that the number of supersymmetries of IIB black hole horizons is N=2 N_- + 2 index(D_\lambda), where index(D_\lambda) is the index of the Dirac operator twisted with the line bundle \lambda^{1/2} 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_- is nonzero, then index(D_\lambda) is non-negative, 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 AdS_2 X S.