Monopole operators and Hilbert series of Coulomb branches of 3d $ \mathcal{N} $ = 4 gauge theories

106

230

Abstract:We introduce several families of N = (2, 2) UV boundary conditions in 3d N = 4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs-and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studying two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality -an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.

Section: Coulomb-branch Imagementioning

confidence: 99%

Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 $$ \mathcal{N}=4 $$ gauge theory

Bullimore

Dimofte

Gaiotto

et al. 2016

106

230

“…In relation to the present AdS 4 /CFT 3 case, it would be interesting to investigate Wilson loops, vortex operators [72] and other subtle CFT aspects -see for example [73][74][75], to understand, in particular, how our solutions capture these fine-points. The study of the spectrum of glueballs and mesons using our backgrounds (both the one obtained via non-Abelian T-duality and the completed one) is also of potential interest to learn about the nature of the duality.…”

Section: Jhep11(2016)133mentioning

confidence: 99%

Three-dimensional N = 4 $$ \mathcal{N}=4 $$ linear quivers and non-Abelian T-duals

Lozano

Macpherson

Montero

et al. 2016

116

In this paper we construct a new Type IIB background with an AdS 4 factor that preserves N = 4 Supersymmetry. This solution is obtained using a non-Abelian T-duality transformation on the Type IIA reduction of the AdS 4 × S 7 background. We interpret our configuration as a patch of a more general background with localised sources, dual to the renormalisation fixed point of a Tρ ρ (SU(N )) quiver field theory. This relates explicitly the AdS 4 geometry to a D3-D5-NS5 brane intersection, illuminating what seems to be a more general phenomenon, relating AdS p+1 backgrounds generated by non-Abelian T-duality to Dp-D(p + 2)-NS5 branes intersections.

“…As discussed in [9,16], the Coulomb branch is generated by a subset of BPS monopole operators with magnetic charges (0, . .…”

Section: Jhep05(2018)114mentioning

confidence: 99%

Good IR duals of bad quiver theories

Dey

Koroteev

2018

The infrared dynamics of generic 3d N = 4 bad theories (as per the goodbad-ugly classification of Gaiotto and Witten) are poorly understood. Examples of such theories with a single unitary gauge group and fundamental flavors have been studied recently, and the low energy effective theory around some special point in the Coulomb branch was shown to have a description in terms of a good theory and a certain number of free hypermultiplets. A classification of possible infrared fixed points for bad theories by Bashkirov, based on unitarity constraints and superconformal symmetry, suggest a much richer set of possibilities for the IR behavior, although explicit examples were not known. In this note, we present a specific example of a bad quiver gauge theory which admits a good IR description on a sublocus of its Coulomb branch. The good description, in question, consists of two decoupled quiver gauge theories with no free hypermultiplets.