D_n Quivers From Branes

TL;DR

Using brane configurations with orbifolds, the paper investigates gauge theories with eight supercharges in $d=3$ and $d=4$, revealing dualities, IR deformations, and exact solutions. It proves a 3d mirror symmetry for $Sp(k)$ with an antisymmetric tensor and $n$ fundamentals via IIB S-duality, uncovering hidden FI deformations in the IR. It constructs and solves a class of finite $N=2$ $d=4$ theories—$D_n$ quivers—via Hitchin systems on orbifold Riemann surfaces, linking their Seiberg-Witten data to $(SO(2n)$ instantons on ${f R}^2 imes T^2)$. The duality structure is shown to be encoded in the moduli space of flat $SO(2n)$ connections on ${T}^2$, consistent with geometric engineering expectations. These results illuminate how brane setups encode nonperturbative dynamics and dualities in low-dimensional supersymmetric gauge theories.

Abstract

D-branes can end on orbifold planes if the action of the orbifold group includes (-1)^{F_L}. We consider configurations of D-branes ending on such orbifolds and study the low-energy theory on their worldvolume. We apply our results to gauge theories with eight supercharges in three and four dimensions. We explain how mirror symmetry for N=4 d=3 gauge theories with gauge group Sp(k) and matter in the antisymmetric tensor and fundamental representations follows from S-duality of IIB string theory. We argue that some of these theories have hidden Fayet-Iliopoulos deformations, not visible classically. We also study a class of finite N=2 d=4 theories (so-called D_n quiver theories) and find their exact solution. The integrable model corresponding to the exact solution is a Hitchin system on an orbifold Riemann surface. We also give a simple derivation of the S-duality group of these theories based on their relationship to SO(2n) instantons on R^2\times T^2.

Figures (6)

• Figure 1: (a) The dash-dotted lines are orbifold 5-planes. The solid vertical lines are NS5-branes. The solid horizontal lines are D3-branes. The horizontal direction corresponds to $x^6$, while the vertical direction corresponds to $x^3,\,x^4,$ and $x^5$ collectively. (b) $D_n$ quiver diagram encoding the gauge group and matter content of the low-energy theory on the branes. Each node corresponds to a unitary group, and the labels on them specify their rank. The solid lines connecting the nodes correspond to bifundamental hypermultiplets.
• Figure 2: The S-dual of the configuration in Figure 1a. The dashed lines are $O5^-$ planes, the solid vertical lines are D5-branes, the solid horizontal lines are D3-branes. For clarity we moved D5-branes slightly away from the orientifold planes. We are working on the double cover of the orientifold background, but only part of it is shown in the picture. In particular, the mirror images of only two D5-branes are shown.
• Figure 3: (a) Brane construction of the mirror for $Sp(k)$ gauge theory with an antisymmetric tensor and $n$ fundamentals. The notation is the same as in Figure 1. (b) Quiver diagram encoding the gauge group and matter content of the brane configuration on the left.
• Figure 4: (a) The brane construction of the mirror for $Sp(k)$ gauge theory with an antisymmetric tensor and $3$ fundamentals. The notation is the same as in Figure 1. (b) Quiver diagram encoding the gauge group and matter content of the brane configuration on the left.
• Figure 5: (a) The brane construction of the mirror for $Sp(k)$ gauge theory with an antisymmetric tensor and $2$ fundamentals. The notation is the same as in Figure 1. (b) Quiver diagram encoding the gauge group and matter content of the brane configuration on the left.