String-scale UV cut-off in the gravitational path integral removes string-coupling dependence from the BPS black hole index in extended supergravity, matching supersymmetry expectations for zero-Euler-number cases.
Generalized Mirror Symmetry and Quantum Black Hole Entropy
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We find general relations between the on-shell gravitational trace anomaly A_N, and the logarithmic correction Delta S_N 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 A_N = 0), we obtain the result DeltaS_N = - Delta S_(8-N) = 2 - N/2, whereas for generic theories the trace anomaly tildeA_N of the fully dualized theory turns out to coincide with 2Delta S_N, up to a model-independent shift: tildeA_N = 2Delta S_N - 1. We also speculate on N=1 theories displaying "large" extremal black hole solutions.
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Extended Supergravity Needs String Scale Cut-off
String-scale UV cut-off in the gravitational path integral removes string-coupling dependence from the BPS black hole index in extended supergravity, matching supersymmetry expectations for zero-Euler-number cases.