On integrable structure and geometric transition in supersymmetric gauge theories

Abstract

We generalize the exact field theoretic correspondence proposed in [1] and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field theories can be recast as a special limit of the refined geometric transition relating open and closed topological string partition functions. We realize the simplest examples of the correspondence explicitly in terms of open-closed geometric transition.arXiv:1303.4237v2 [hep-th]

Quantum integrability from non-simply laced quiver gauge theory

“…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.…”

Refined geometric transition and qq-characters

“…However, we claim in this paper that the refined geometric transition should be sensitive to where the preferred direction is set. To explain this point, at first we give a brief review of the prescription for the refined geometric transition that has been used in the literatures [34,16,35,36,37,38] in Section 2.1, and then Section 2.2 contains our proposal that actually clarifies the effect of the different selection of the preferred direction. The quantitative argument which we rely on is shown in Section 2.3.…”

“…In this paper we propose how to realize the qq-character in refined topological string by the brane insertion, analyzed using the refined geometric transition. In particular, the codimension-2 defect operator, corresponding to the surface operator in gauge theory, is obtained by inserting a defect brane to the Lagrangian submanifold of the Calabi-Yau threefold [34,16,35,36,37,38]. We show that the Y-operator, which is a codimension-4 building block of the qq-character, can be constructed by inserting two codimension-2 defect operators.…”

Refined toric branes, surface operators and factorization of generalized Macdonald polynomials

“…We consider refined toric branes wrapping Lagnangian submanifolds inside a toric CY three-fold [43]. As is well-known, this setup corresponds to surface operators in gauge theory and to degenerate fields of the W N -algebra [44][45][46][47][48][49][50][53][54][55]. We will consider mostly the algebraic side of the problem and relate the stack of refined branes on the preferred leg of the toric diagram to a particular intertwining operator of DIM algebra, which can be recast into a combination of generalized Macdonald polynomials [56,59].…”