Aspects of defects in 3d-3d correspondence

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: Future Directionsmentioning

confidence: 99%

Rotating black hole entropy from M5-branes

Benini

Gang

Zayas

2020

Self Cite

“…In particular, we find that for an even number of walls, if all external legs of the skeleton diagrams are closed, the theories associated with the same topology of the skeleton diagram (for given rank and CS levels of the gauge groups) are dual to each other, independent of the way we glue the basic building block (2.7). The gluing performed in this paper can also be viewed as a generalisation of the S-fold theory [27][28][29][30][31] associated with duality walls in the 4d N = 4 super-Yang-Mills to a theory with lower amounts of supersymmetry, which is the 4d N = 2 gauge theory in our case.…”

Section: Discussionmentioning

confidence: 99%

Duality walls in the 4d $$ \mathcal{N} $$ = 2 SU(N) gauge theory with 2N flavours

Garozzo

Mekareeya

Sacchi

2019

S-duality domain walls are extended objects in supersymmetric gauge theories with several rich physical properties. This paper focuses on 3d N = 2 gauge theories associated with S-duality walls in the 4d N = 2 SU (N ) gauge theory with 2N flavours. The theories associated with multiple duality walls are constructed by gluing together a basic building block, which is the theory associated with a single duality wall. We propose the prescription for gluing many copies of such a basic building block together as well as present the prescription for self-gluing. A number of dualities between such theories are discovered and studied using the supersymmetric index. This work generalises the notion of the S-fold theory, which has been so far studied extensively in the context of duality walls in the 4d super-Yang-Mills theory, to the theory with lower amounts of supersymmetry. arXiv:1909.02832v1 [hep-th] 6 Sep 2019 7 Conclusion and perspectives 35 A 3d supersymmetric index 36 -1 -

“…In terms of SL(N, C) Chern-Simons theory, ρ specifies a monodromy defect on C, while the weights λ,λ correspond to Wilson loops in irreducible representations of the subgroup of SL(N, C) left unbroken by the monodromy defect [48,49].…”

Section: Discussionmentioning

confidence: 99%

Refined 3d-3d correspondence

Alday

Genolini

Bullimore

et al. 2017

We explore aspects of the correspondence between Seifert 3-manifolds and 3d N = 2 supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d N = 2 theories constructed from boundary conditions and interfaces in a 4d N = 2 * theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-'t Hooft loops in the 4d N = 2 * theory. In the presence of a mass parameter for the distinguished flavour symmetry, we recover aspects of refined Chern-Simons theory with complex gauge group, and in particular construct an analytic continuation of the S-matrix of refined Chern-Simons theory.