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arXiv · 1306.5765

Index theory and dynamical symmetry enhancement near IIB horizons

U. Gran·J. Gutowski·G. Papadopoulos
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Abstract

We show that the number of supersymmetries of IIB black hole horizons is N=2 N_- + 2 index(D_λ), where index(D_λ) is the index of the Dirac operator twisted with the line bundle λ^{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_λ) 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.

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U. Gran, J. Gutowski, G. Papadopoulos. 2013-06-24. Index theory and dynamical symmetry enhancement near IIB horizons. https://doi.org/10.1007/jhep11(2013)104

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