Generalized mirror symmetry and quantum black hole entropy

We find general relations between the on-shell gravitational trace anomaly AN, and the logarithmic correction ΔSN to the entropy of “large” BPS extremal black holes in N⩾2 supergravity theories in D=4 space-time dimensions (recently computed by Sen, 2011 [1]). For (generalized) self-mirror theories (all having AN=0), we obtain the result ΔSN=−ΔS8−N=2−N/2, whereas for generic theories the trace anomaly A˜N of the fully dualized theory turns out to coincide with 2ΔSN, up to a model-independent shift: A˜N=2ΔSN−1. We also speculate on N=1 theories displaying “large” extremal black hole solutions.