Abstract

We study the large N expansion of twisted partition functions of 3d mathcal{N} = 2 superconformal field theories arising from N M5-branes wrapped on a hyperbolic 3- manifold, M3. Via the 3d-3d correspondence, the partition functions of these 3d mathcal{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 PSL(N, ℂ) Chern-Simons theory around irreducible flat connections on M3. Using mathematical results on the asymptotics of the invariants, we compute the twisted partition functions in the large N limit including perturbative corrections to all orders in 1/N . Surprisingly, the perturbative expansion terminates at finite order. The leading part of the partition function is of order N3 and agrees with the Bekenstein-Hawking entropy of the dual black holes. The subleading part, in particular the log N -terms in the field theory partition function is found to precisely match the one-loop quantum corrections in the dual eleven dimensional supergravity. The field theory results of other terms in 1/N provide a stringent prediction for higher order corrections in the holographic dual, which is M-theory.

Highlights

  • Most of these results have been propelled by an improved understanding of threedimensional N = 2 supersymmetric field theories thanks to supersymmetric localization, see [9,10,11] for the original developments and [12,13,14,15] for some recent relevant applications

  • 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, M3

  • To help acquaint the reader with the M5 duality we present a comparison with the more standard form of AdS4/CFT3 based on M2-branes probing a cone over a Sasakian-Einstein 7-manifold Y7 in table 1

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Summary

Holography for wrapped M5-branes

A peculiarity of AdS4/CFT3 from M5-branes is that we can use the 3d-3d correspondence [17, 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] which provides an alternative way of computing some supersymmetic quantities, using geometry. The absence of flavor symmetry implies that in the partition functions there are no extra fugacities and, we are limited to the universal sector This is precisely the situation described in [7], albeit from a different embedding point of view, as we will discussed below

Holographic dual
Twisted partition functions dual to wrapped M5 branes
Taub-Bolt solutions in AdS4
Magnetically charged black hole in AdS4
Derivation
Consistency check: integrality of twisted indices
Two dominant Bethe-vacua from the hyperbolic structure
Logarithmic corrections from supergravity
Robustness of logarithmic terms in one-loop effective actions
Zero-mode contributions
The one-loop effective action and logarithmic correction
Conclusions
Full Text
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