Mixed ’t Hooft anomalies and the Witten effect for AdS black holes - Matthew Heydeman; Chiara Toldo (Journal of High Energy Physics)
Abstract For a variety of BPS black holes in string theory, the supersymmetric index has provided a microscopic validation of the Bekenstein-Hawking formula. In the near-BPS limit, a gravitational path integral analysis previously revealed the semiclassical spectrum is modified, having a large extremal degeneracy (consistent with the index) and a mass gap up to a continuum of non-BPS black holes. Presently, we study examples in which these sharp features of the spectrum are altered due to the presence of anomalies in the form of ϑ-angle terms in the action. These may appear generally, but we focus on near-BPS dyonic AdS4 black holes in M-theory, dual to 3d N $$ \mathcal{N} $$ = 2 SCFTs of Class R obtained by twisted compactification of N wrapped M5 branes. Due to the Witten effect, the dyonic black holes receive quantum corrections to their charges, and when ϑ = π one may find a mixed ‘t Hooft anomaly between the U(1) R and ℤ 2 time reversal symmetries. Using results from N $$ \mathcal{N} $$ = 2 JT supergravity, we find these effects result in a spectrum in which both the gap and index are reduced, and may even vanish. Surprisingly, for ϑ → π, neither the Bekenstein-Hawking formula nor the index correctly account for the extremal degeneracies.