2020 # Precision microstate counting for the entropy of wrapped M5-branes

**Abstract:** We study the large N expansion of twisted partition functions of 3d N = 2 superconformal field theories arising from N M5-branes wrapped on a hyperbolic 3manifold, M 3 . Via the 3d-3d correspondence, the partition functions of these 3d N = 2 superconformal field theories are related to simple topological invariants on the 3-manifold. The partition functions can be expressed using only classical and one-loop perturbative invariants of P SL(N, C) Chern-Simons theory around irreducible flat connections on M 3 . U…

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“…On the other hand, we will propose the 3d-3d relation for the refined version of the twisted index, with non-trivial supporting evidence. Motivated by that, we will also propose a 3d-3d relation for the twisted index on general Riemann surfaces, which generalizes previous work [20] to cover more general classes of 3-manifolds M 3 . Finally, in subsection 2.4 we will provide non-trivial consistency checks for the proposed 3d-3d relations, confirming the integral properties of the various indices.…”

confidence: 83%

“…On the other hand, we will propose the 3d-3d relation for the refined version of the twisted index, with non-trivial supporting evidence. Motivated by that, we will also propose a 3d-3d relation for the twisted index on general Riemann surfaces, which generalizes previous work [20] to cover more general classes of 3-manifolds M 3 . Finally, in subsection 2.4 we will provide non-trivial consistency checks for the proposed 3d-3d relations, confirming the integral properties of the various indices.…”

confidence: 83%

“…While in [20] the 3d-3d relation was proposed for 3-manifolds with vanishing H 1 (M 3 , Z N ), here we generalize it to arbitrary closed hyperbolic 3-manifolds.…”

confidence: 85%