Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Duality and enhancement of symmetry in 5d gauge theories

Gabi Zafrir

TL;DR

This paper investigates dualities and symmetry enhancements in 5d $\mathcal{N}=1$ gauge theories using brane-web constructions and exact 5d superconformal index calculations. The authors show that instanton sectors drive nonperturbative symmetry enhancements (including to exceptional groups like $G_2$) and provide detailed index matches across multiple dual pairs, including quivers with additional $SU(3)$ nodes. By computing perturbative plus instanton contributions and carefully removing decoupled states, they demonstrate a rich network of dualities with consistent quantum global symmetries. The work advances understanding of UV fixed points in 5d theories and suggests broad generalizations to higher-node quivers and potential holographic connections.

Abstract

We study various cases of dualities between $\cal{N}$$=1$ 5d supersymmetric gauge theories. We motivate the dualities using brane webs, and provide evidence for them by comparing the superconformal index. In many cases we find that the classical global symmetry is enhanced by instantons to a larger group including one where the enhancement is to the exceptional group $G_2$.

Duality and enhancement of symmetry in 5d gauge theories

TL;DR

This paper investigates dualities and symmetry enhancements in 5d gauge theories using brane-web constructions and exact 5d superconformal index calculations. The authors show that instanton sectors drive nonperturbative symmetry enhancements (including to exceptional groups like ) and provide detailed index matches across multiple dual pairs, including quivers with additional nodes. By computing perturbative plus instanton contributions and carefully removing decoupled states, they demonstrate a rich network of dualities with consistent quantum global symmetries. The work advances understanding of UV fixed points in 5d theories and suggests broad generalizations to higher-node quivers and potential holographic connections.

Abstract

We study various cases of dualities between 5d supersymmetric gauge theories. We motivate the dualities using brane webs, and provide evidence for them by comparing the superconformal index. In many cases we find that the classical global symmetry is enhanced by instantons to a larger group including one where the enhancement is to the exceptional group .

Paper Structure

This paper contains 10 sections, 51 equations, 19 figures, 1 table.

Table of Contents

  1. Introduction
  2. The superconformal index
  3. Adding more flavor
  4. Index calculation
  5. Enhancement of symmetry in $SU(2)\times USp(6)$
  6. Inserting an $SU(3)$ group
  7. Index calculation
  8. Two extra nodes
  9. Conclusions
  10. Determining gauge theory parameters from the web

Figures (19)

  • Figure 1: (a) The brane web for $SU(2)\times SU(2)$. (b) Going along the Coulomb branch of the left $SU(2)$ the right one eventually becomes strongly coupled. The arrow shows the D-string becoming massless at that strong coupling point. (c) Doing an S-duality transformation results in the web for $SU(3)+2F$ and one can continue past the singularity.
  • Figure 2: (a) The brane web for $SU_{\pi}(2)\times SU(2)+2F$. (b) The S-dual web which describes $SU_1(3)+4F$. The dotted lines show the D1-strings corresponding to decoupled states.
  • Figure 3: (a) The brane web for $1F+SU(2)\times SU(2)+1F$. (b) The S-dual web which describes $SU_0(3)+4F$. The dotted lines show the D1-strings corresponding to decoupled states.
  • Figure 4: The brane web for $SU_{\pi}(2)\times SU_0(3)\times SU_{0}(2)$. (a) The web at a generic point on the moduli space. (b) The web deformed as to exhibit the quiver structure.
  • Figure 5: The brane web for $SU_{\pi}(2)\times SU_{-1}(3)\times SU_{\pi}(2)$. (a) The web at a generic point on the moduli space. (b) The web deformed as to exhibit the quiver structure.
  • ...and 14 more figures