Abstract
Many three-dimensional mathcal{N}=2 SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces. We exploit this fact to derive a universal formula which relates the planar limit of the topologically twisted index of these SCFTs and their three-sphere partition function. We then utilize this to account for the entropy of a large class of supersymmetric asymptotically AdS4 magnetically charged black holes in M-theory and massive type IIA string theory. In this context we also discuss novel AdS2 solutions of eleven-dimensional supergravity which describe the near horizon region of large new families of supersymmetric black holes arising from M2-branes wrapping Riemann surfaces.
Highlights
M-theory and massive type IIA modelsThe derivation of (2.9) is based on the large N identities (2.5) and (2.6), which in turn can be established for a large class of Yang-Mills-Chern-Simons theories with fundamental and bi-fundamental chiral fields with M-theory or massive type IIA duals
Many three-dimensional N = 2 SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces
The universality of this relation stems from a universal partial topological twist that is used in the definition of the twisted index
Summary
The derivation of (2.9) is based on the large N identities (2.5) and (2.6), which in turn can be established for a large class of Yang-Mills-Chern-Simons theories with fundamental and bi-fundamental chiral fields with M-theory or massive type IIA duals. Under the same conditions, the topologically twisted index scales like N 3/2 and the identities (2.5) and (2.6) are valid [6] This particular class of quivers include all the vector-like examples in [41–43] and many of the flavored theories in [44, 45]. For the “chiral” theories discussed in [41–43], on the other hand, it is not known how to properly take the large N limit in the matrix model to obtain the correct scaling predicted by holography This applies both for the topologically twisted index and for the S3 partition function. The dual field theory is obtained by considering the four-dimensional theory dual to AdS5× SE5, where SE5 is the five-dimensional Sasaki-Einstein with local base KE4, reducing it to three dimensions and adding a Chern-Simons term with level k for all gauge groups.. The same holds for the theory in [53] and some of its generalizations in massive type IIA.
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