A 5d/3d duality from relativistic integrable system

We study half-BPS surface operators in supersymmetric gauge theories in four and five dimensions following two different approaches. In the first approach we analyze the chiral ring equations for certain quiver theories in two and three dimensions, coupled respectively to four-and five-dimensional gauge theories. The chiral ring equations, which arise from extremizing a twisted chiral superpotential, are solved as power series in the infrared scales of the quiver theories. In the second approach we use equivariant localization and obtain the twisted chiral superpotential as a function of the Coulomb moduli of the four-and five-dimensional gauge theories, and find a perfect match with the results obtained from the chiral ring equations. In the five-dimensional case this match is achieved after solving a number of subtleties in the localization formulas which amounts to choosing a particular residue prescription in the integrals that yield the Nekrasov-like partition functions for ramified instantons. We also comment on the necessity of including ChernSimons terms in order to match the superpotentials obtained from dual quiver descriptions of a given surface operator.

Section: Adding Chern-simons Termsmentioning

confidence: 99%

Surface operators, chiral rings and localization in $$ \mathcal{N} $$ =2 gauge theories

Ashok

Billó

Dell’Aquila

et al. 2017

“…The expectation value in the last term of (4.2) is taken in the 5d SU(N ) gauge theory and the function (z) obeys the relation ∂ z (z) = log 2 sinh βzIn each 3d node of the quiver we can turn on a Chern-Simons term with coupling k I . Upon circle compactification, these Chern-Simons terms give rise to an additional term in the superpotential which is[69]…”

mentioning

confidence: 99%

Surface operators in 5d gauge theories and duality relations

Ashok

Billó

Dell’Aquila

et al. 2018

We study half-BPS surface operators in 5d N = 1 gauge theories compactified on a circle. Using localization methods and the twisted chiral ring relations of coupled 3d/5d quiver gauge theories, we calculate the twisted chiral superpotential that governs the infrared properties of these surface operators. We make a detailed analysis of the localization integrand, and by comparing with the results from the twisted chiral ring equations, we obtain constraints on the 3d and 5d Chern-Simons levels so that the instanton partition function does not depend on the choice of integration contour. For these values of the Chern-Simons couplings, we comment on how the distinct quiver theories that realize the same surface operator are related to each other by Aharony-Seiberg dualities.

“…Furthermore, if d ij = d j , the saddle point equation in the NS 2 limit is reduced as Here we also comment on how the same sets of Bethe ansatz equations (5.36) can also arise from the saddle point equations for the twisted superpotentials of the appropriate N = 2 supersymmetric gauge theories compactified on R 2 × S 1 , this is in the same vein as the 3d/5d correspondence considered in [37,38]: While in our current situation, the corresponding Dbrane construction, hence definite interpretation of them as the world volume theories of codimension two defects are currently lacking, we nevertheless write down these compactified three dimensional theories for possible references.…”

Section: Root Of Higgs Branch and Truncation Of Bethe Rootsmentioning

confidence: 69%

“…We now tune the Coulomb moduli parameter to impose the quantization condition at the root of Higgs branch in the NS 1 limit [35,36,37]:…”

Section: Root Of Higgs Branch and Truncation Of Bethe Rootsmentioning

confidence: 99%

Quantum integrability from non-simply laced quiver gauge theory

Chen

Kimura

2018

Self Cite

We consider the compactifcation of 5d non-simply laced fractional quiver gauge theory constructed in [1]. In contrast to the simply laced quivers, here two Ω-background parameters play different roles, so that we can take two possible Nekrasov-Shatashvili limits. We demonstrate how different quantum integrable systems can emerge from these two limits, using BC 2 -quiver as the simplest illustrative example for our general results.We also comment possible connections with compactified 3d non-simply laced quiver gauge theory.