3d N = 2 $$ \mathcal{N}=2 $$ minimal SCFTs from wrapped M5-branes

Self Cite

We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class $$ \mathrm{\mathcal{R}} $$ ℛ . Using results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d correspondence we are able to constrain the two independent coefficients in the four-derivative supergravity Lagrangian. This in turn allows us to calculate the subleading terms in the large-N expansion of supersymmetric partition functions for an infinite class of three-dimensional $$ \mathcal{N} $$ N = 2 SCFTs of class $$ \mathrm{\mathcal{R}} $$ ℛ . We also determine the leading correction to the Bekenstein-Hawking entropy of asymptotically AdS4 black holes arising from wrapped M5-branes. In addition, we propose and test some conjectures about the perturbative partition function of Chern-Simons theory with complexified ADE gauge groups on closed hyperbolic three-manifolds.

Section: Jhep04(2021)058mentioning

confidence: 77%

Higher-derivative supergravity, wrapped M5-branes, and theories of class $$ \mathrm{\mathcal{R}} $$

Bobev

Charles

Gang

et al. 2021

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“…Perturbative invariants from State-integral model Using the topological nature of Chern-Simons theory, its path-integral can be reduced to a finite dimensional integral which are called state-integral model. See [37][38][39][82][83][84][85] for state-integral models of SL(N, C) Chern-Simons theory from which the perturbative invariants {S α n [M 3 ; N ]} can be efficiently computed. The state-integral model is turned out to be equal to the localization integral for T N [M 3 ] on squashed 3-sphere S 3 b [86] with the identification = 2πib 2 .…”

Section: Acknowledgmentsmentioning

confidence: 99%

Rotating black hole entropy from M5-branes

Benini

Gang

Zayas

2020

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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)

“…Arguably the most important numerical bootstrap result is the precise determination of the critical exponents of the three-dimensional Ising and O(N ) models [48,[50][51][52][53][54][55]. In the supersymmetric literature, one can find studies of 3d models with minimal supersymmetry [56][57][58], N = 2 supersymmetry [59][60][61][62][63] and maximal N = 8 supersymmetry [64][65][66][67]. Similarly, in four dimensions there have been studies of N = 1 theories [42,49,[68][69][70], N = 2 theories [12][13][14], N = 3 theories [71] and of N = 4 SYM theory [72,73].…”

Section: Numerical Boundsmentioning

confidence: 99%

Bootstrapping Coulomb and Higgs branch operators

Liendo

2021

We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in 4d$$ \mathcal{N} $$ N = 2 superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In particular, we present improved bounds on OPE coefficients for some selected Argyres-Douglas models, and compare them to recent work where the same cofficients were obtained in the limit of large r charge. There is solid agreement between all the approaches. The improved bounds can be used to extract an approximate spectrum of the Argyres-Douglas models, which can then be used as a guide in order to corner these theories to numerical islands in the space of conformal dimensions. When there is a flavor symmetry present, we complement the analysis by including mixed correlators of Coulomb branch operators and the moment map, a Higgs branch operator which sits in the same multiplet as the flavor current. After calculating the relevant superconformal blocks we apply the numerical machinery to the mixed system. We put general constraints on CFT data appearing in the new channels, with particular emphasis on the simplest Argyres-Douglas model with non-trivial flavor symmetry.