Generalized Mirror Symmetry and Quantum Black Hole Entropy
Abstract
We find general relations between the on-shell gravitational trace anomaly AN, and the logarithmic correction Delta SN to the entropy of "large" BPS extremal black holes in N>1 supergravity theories in D=4 space-time dimensions (recently computed by Sen [arXiv:1108.3842]). For (generalized) self-mirror theories (all having AN = 0), we obtain the result DeltaSN = - Delta S(8-N) = 2 - N/2, whereas for generic theories the trace anomaly tildeAN of the fully dualized theory turns out to coincide with 2Delta SN, up to a model-independent shift: tildeAN = 2Delta SN - 1. We also speculate on N=1 theories displaying "large" extremal black hole solutions.
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