Precision microstate counting for the entropy of wrapped M5-branes

Self Cite

We compute the superconformal index of 3d N = 2 superconformal theories obtained from N M5-branes wrapped on a hyperbolic 3-manifold. Exploiting the 3d-3d correspondence we use perturbative invariants of SL(N, C) Chern-Simons theory to determine the superconformal index in the large N limit, including logarithmic in N corrections. The leading order partition function provides a microscopic foundation for the entropy function of the dual rotating asymptotically AdS 4 black holes. We also verify that the supergravity one-loop contribution to the log N term coincides with the field theoretic result. We also propose a 3d-3d formulation for the refined topologically twisted index and provide strong evidence in support of its vanishing which agrees with the fact that the expected dual rotating magnetically charged black hole does not exist, thus providing an interesting link between gravity and a tantalizing mathematical result. 3d T N [M 3 ] theoryWe start with the definition and basic properties of the 3d T N [M 3 ] theory appearing on the LHS of the 3d-3d relation (2.1). We define T N [M 3 ] := the 3d N = 2 superconformal field theory obtained from a twisted compactification of the 6d A N −1 (2,0) theory on M 3 , M 3 = a closed hyperbolic 3-manifold = H 3 /Γ .(2.2)

Section: D-3d Relations For 3d Indicesmentioning

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.…”

Section: (235)mentioning

confidence: 85%

Section: Refined Twisted Indexmentioning

confidence: 96%

Section: Refined Twisted Indexmentioning

confidence: 99%

“…The torsion can be computed from the following formula (see the appendix of [20] for the derivation):…”

Section: Integer Expansion Of the Twisted Indexmentioning

confidence: 99%

See 3 more Smart Citations

Rotating black hole entropy from M5-branes

Benini

Gang

Zayas

2020

Self Cite

Sub-leading structures in superconformal indices: subdominant saddles and logarithmic contributions

Lezcano

Hong

Liu

et al. 2021

Self Cite

We systematically study various sub-leading structures in the superconformal index of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU(N) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be log N, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d $$ \mathcal{N} $$ N = 1 superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form log N. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS5 black holes and could be tested by low-energy IIB supergravity.

Wrapped M5-branes and complex saddle points

Genolini

2022

We study the effects of the introduction of a ϑ term in minimal gauged supergravity in four dimensions. We show why this term is not present in supergravity duals of field theories arising on wrapped M2-branes, but is there in the case of M5-branes wrapping hyperbolic manifolds Σ3, and compute the higher-derivative corrections. Having proved that the on-shell supergravity action of any supersymmetric solution can be expressed in terms of data from the fixed points of a Killing vector, we show that it is proportional to a complex topological invariant of Σ3. This is consistent with the characteristics of the dual three-dimensional 𝒩= 2 SCFT predicted by the 3d-3d correspondence, and we match the large N limit of its partition functions in the known cases.