5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory

TL;DR

This work demonstrates that 5d ${\cal N}=1$ fixed points realized via 5-brane webs exhibit non-perturbative global symmetry enhancements, such as $SU(2)$ in ${SU(N)}_N$ and larger groups in quiver theories, revealed through careful computation of the 5d superconformal index. By combining web moves (continuation past infinite coupling) with exact index calculations, including instanton corrections via Nekrasov functions, the authors establish dualities between quiver and non-quiver theories and map charge correspondences between dual frames. They develop and apply techniques to handle subtleties in instanton counting, including the removal of decoupled states and handling of parallel external branes, and verify dualities up to high instanton orders across several generalizations (higher ranks, extra flavors, extra nodes). The results illuminate how brane constructions, non-perturbative dynamics, and protected indices jointly inform the landscape of 5d fixed points, with potential implications for higher-rank dualities and connections to holographic realizations in AdS$_6$ contexts.

Abstract

We present a number of investigations of 5d ${\cal N}=1$ supersymmetric gauge theories that make use of 5-brane web constructions and the 5d superconformal index. These include an observation of enhanced global symmetry in the 5d fixed point theory corresponding to $SU(N)$ gauge theory with Chern-Simons level $\pm N$, enhanced global symmetries in quiver theories, and dualities between quiver theories and non-quiver theories. Instanton contributions play a crucial role throughout.

Figures (17)

• Figure 1: $SU(2)$ webs. (a) $SU(2)_0$ "$E_1$ theory", (b) $SU(2)_\pi$ "$\tilde{E}_1$ theory"
• Figure 2: $SU(3)$ webs with CS level $\kappa = 0,1,2$.
• Figure 3: Positive and negative deformations of the $SU(2)$ theories.
• Figure 4: Webs with parallel external 5-branes. The dashed line corresponds to the decoupled state.
• Figure 5: Webs for $SU(N)_N$ with $N=1,2$ and $3$.