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Abstract: In four dimensional string theories with N=4 and N=8 supersymmetries one canoften define twisted index in a subspace of the moduli space which capturesadditional information on the partition function than the ones contained in theusual helicity trace index. We compute several such indices in type IIB stringtheory on K3 x T^2 and T^6, and find that they share many properties with theusual helicity trace index that captures the spectrum of quarter BPS states inN=4 supersymmetric string theories. In particular the partition function is amodular form of a subgroup of Sp2,Z and the jumps across the walls ofmarginal stability are controlled by the residues at the poles of the partitionfunction. However for large charges the logarithm of this index grows as 1-ntimes the entropy of a black hole carrying the same charges where n is theorder of the symmetry generator that is used to define the twisted index. Weprovide a macroscopic explanation of this phenomenon using quantum entropyfunction formalism. The leading saddle point corresponding to the attractorgeometry fails to contribute to the twisted index, but a Z n orbifold of theattractor geometry produces the desired contribution.

Autor: Ashoke Sen

Fuente: https://arxiv.org/


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