F-Theory, spinning black holes and multi-string branches

Abstract

We study 5d supersymmetric black holes which descend from strings of generic N = (1, 0) supergravity in 6d. These strings have an F-theory realization in 6d as D3 branes wrapping smooth genus g curves in the base of elliptic 3-folds. They enjoy (0, 4) worldsheet supersymmetry with an extra SU(2) L current algebra at level g realized on the left-movers. When the smooth curves degenerate they lead to multi-string branches and we find that the microscopic worldsheet theory flows in the IR to disconnected 2d CFTs having different central charges. The single string sector is the one with maximal central charge, which when wrapped on a circle, leads to a 5d spinning BPS black hole whose horizon volume agrees with the leading entropy prediction from the Cardy formula. However, we find new phenomena where this branch meets other branches of the CFT. These include multi-string configurations which have no bound states in 6 dimensions but are bound through KK momenta when wrapping a circle, as well as loci where the curves degenerate to spheres. These loci lead to black hole configurations which can have total angular momentum relative to a Taub-Nut center satisfying J 2 > M 3 and whose number of states, though exponentially large, grows much slower than those of the large spinning black hole.

F-theory and AdS3/CFT2

“…It is in general an interesting question to characterise systematically such Type IIB solutions, as a method for exploring superconformal field theories (SCFTs). Moreover, recently 1 various D3-brane configurations in F-theory have been shown to give rise to 2d SCFTs [5][6][7][8][9]. These constructions are based on D3-branes wrapped on a complex curve C in the base B d−1 of the elliptic fibration.…”

Squashed Toric Sigma Models and Mock Modular Forms

“…This route was used to study the elliptic genus of ALE and ALF spaces in [25], and the answer thus obtained is a Jacobi form meromorphic in the elliptic variable u. This meromorphicity is related to the fact that the scale introduced by the background Wilson line u mildly breaks the infinite-dimensional superconformal algebra, as can be seen from the fact that bosons can no longer be separated into left-and right-moving parts [26,27]. In this paper we take a different route.…”

Mixed Rademacher and BPS black holes

“…For instance, our results might be extended to the mixed mock modular forms arising in compactifications of string theory on CY 3 -folds leading to four-dimensional black holes with N = 2 supersymmetry [68], or the related five-dimensional spinning black holes [69].…”