3d dualities with decoupled sectors and brane transitions

Abstract

We find exact functional relations among the sphere partition functions of threedimensional N = 4 superconformal Chern-Simons theories with circular quiver diagrams. These relations suggest new dualities in gauge theories which are the products of circular quiver gauge theories and decoupled linear quiver gauge theories. The dualities can be interpreted as simple brane transitions in the Hanany-Witten brane construction in type IIB string theory. Interestingly, the brane transitions cannot be generated by the Hanany-Witten transition or the SL (2, Z) transformation. Our results can be regarded as generalization and clarification of dualities implied from Weyl symmetries of quantum curves. To obtain the exact results, we employ the supersymmetric localization technique and the Fermi gas approach.

M2-branes and $\mathfrak{q}$-Painlevé equations

“…On the mathematical side, it provides new Fredholm determinant expressions for the τ -functions of q-Painlevé equations. Moreover, it is worth to observe that this viewpoint opens a new algebraic characterization of duality symmetries of supersymmetric gauge theories in three dimensions in terms of affine Weyl group associated to the q-difference equations [22,23,24,25]. Finally, we expect this line of thought to shed light on the classification problem of five dimensional superconformal field theories with eight supercharges.…”

Duality Cascades and Affine Weyl Groups

“…We may gain new insights on both brane transitions and quantum curves by relating them directly. Indeed, in studying the partition functions of the generalized ABJM theories, recently new types of brane transitions were proposed [3][4][5]. In this paper we shall turn to subsequent applications of the HW transitions in a circle known as duality cascades and study the processes with Weyl groups.…”

“…Due to this reason, the D 5 and E 7 Weyl groups are subject to the Z 2 folding and reduce respectively to the B 3 and F 4 Weyl groups. Then, we introduce the deformation of FI parameters for full parameters of quantum curves and study the same problem of the 0 1 2 6 3 7 4 8 5 9 [4,8] θ [5,9] θ This paper is organized as follows. We study the cases without deformations of FI parameters in the next section, while turn to the deformation in section 3.…”