Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence

Self Cite

In the presence of an Ω-deformation, local operators generate a chiral algebra in the topological-holomorphic twist of a four-dimensional N = 2 supersymmetric field theory. We show that for a unitary N = 2 superconformal field theory, the chiral algebra thus defined is isomorphic to the one introduced by Beem et al. Our definition of the chiral algebra covers nonconformal theories with insertions of suitable surface defects. 21A Ω-deformations for vector and chiral multiplets 23

“…For a topological twist of an N = (2, 2) supersymmetric field theory, an Ω-deformation may be constructed as follows [16,17].…”

Section: ω-Deformationsmentioning

confidence: 99%

Chiral algebras from Ω-deformation

Yagi

2019

Self Cite

“…In the supersymmetric gauge theory T S 3 \Γ 5 , there are 15 dynamical vector multiplet (gauge fields)Ṽ I=1,··· ,15 carrying the gauge group U(1) 15 Both the Chern-Simons level matrices t, s are of integer entries:…”

Section: "T-type"mentioning

confidence: 99%

“…Let's consruct holomorphic block of the 3d supersymmetric gauge theory T S 3 \Γ 5 labelled by the graph complement 3-manifold S 3 \ Γ 5 , which is defined in Section 3.1. T S 3 \Γ 5 has the gauge group U(1) 15 and the flavor symmetry group U(1) 15 . It is straight-forward to obtain the perturbative expression of holomorphic block integral…”

Section: Holomorphic Block Of 3-dimensional Supersymmetric Gauge Theomentioning

confidence: 99%

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4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block

Han¹

2016

A class of 3d N = 2 supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction [1] in 3d-3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class, the massive supersymmetric vacua of the theory contain the classical geometries on a 4d simplicial complex. The corresponding 4d simplicial geometries are locally constant curvature (either dS or AdS), in the sense that they are made by gluing geometrical 4-simplices of the same constant curvature. When the simplicial complex is sufficiently refined, the simplicial geometries can approximate all possible smooth geometries on 4-manifold. At the quantum level, we propose that a class of holomorphic blocks defined in [2] from the 3d N = 2 gauge theories are wave functions of quantum 4d simplicial geometries. In the semiclassical limit, the asymptotic behavior of holomorphic block reproduces the classical action of 4d Einstein-Hilbert gravity in the simplicial context.

“…It turns out that the localization procedure can be conducted in a very similar manner with [10], where the localization of the Ω-deformed two-dimensional Landau-Ginzburg model was discussed. In fact, our localization can be viewed as the gauge theory analogue of [10] on C ⊥ , which was discussed in [28] in its application of recovering four-dimensional Chern-Simons theory from six-dimensional supersymmetric gauge theory (see also [26,27] for the discussion of B-models on the compact disk where the localization locus was chosen to be constant maps), occuring at each point of C. The localization locus is given by solutions to certain gradient flow equations (emanating from the critical point of the superpotential as we take C ⊥ = R 2 ). To obtain the action of the localized theory on C, we have to evaluate the action on this localization locus.…”

Section: Introductionmentioning

confidence: 99%

SCFT/VOA correspondence via Ω-deformation

Jeong

2019

We investigate an alternative approach to the correspondence of four-dimensional N = 2 superconformal theories and two-dimensional vertex operator algebras, in the framework of the Ω-deformation of supersymmetric gauge theories. The two-dimensional Ω-deformation of the holomorphic-topological theory on the product four-manifold is constructed at the level of supersymmetry variations and the action. The supersymmetric localization is performed to achieve a two-dimensional chiral CFT. The desired vertex operator algebra is recovered as the algebra of local operators of the resulting CFT. We also discuss the identification of the Schur index of the N = 2 superconformal theory and the vacuum character of the vertex operator algebra at the level of their path integral representations, using our Ω-deformation point of view on the correspondence.