3d Coulomb branch and 5d Higgs branch at infinite coupling

Giulia Ferlito,Gabi Zafrir,Noppadol Mekareeya,Amihay Hanany

doi:10.1007/jhep07(2018)061

Abstract

The Higgs branch of minimally supersymmetric five dimensional SQCD theories increases in a significant way at the UV fixed point when the inverse gauge coupling is tuned to zero. It has been a long standing problem to figure out how, and to find an exact description of this Higgs branch. This paper solves this problem in an elegant way by proposing that the Coulomb branches of three dimensional mathcal{N}=4 supersymmetric quiver gauge theories, named “Exceptional Sequences”, provide the solution to the problem. Thus, once again, 3d mathcal{N}=4 Coulomb branches prove to be useful tools in solving problems in higher dimensions. Gauge invariant operators on the 5d side consist of classical objects such as mesons, baryons and gaugino bilinears, and non perturbative objects such as instanton operators with or without baryon number. On the 3d side we have classical objects such as Casimir invariants and non perturbative objects such as monopole operators, bare or dressed. The duality map works in a very interesting way.

Highlights

N = 4 quiver gauge theory whose Coulomb branch is precisely H∞
The study of Higgs branches for 5d N = 1 SU(n) theories with Nf flavors already appears in [1] for the special case n = 2. In there it is argued, via a string-theoretic analysis of the D4, D8, O8− brane system, that an SU(2) gauge theory with Nf flavors has a Higgs branch at infinite coupling H∞ which is the reduced moduli space of 1 ENf +1 instanton on C2
The special case of SU(2) SYM with a trivial discrete theta angle, which displays a E1 symmetry at infinite coupling, is discussed in the five brane web description of [4, 19]: in there, the Higgs branch at infinite coupling is realized as a separation of five branes in directions transverse to the web that open up only at infinite coupling

Summary

Introduction

At infinite coupling both mesons and baryons fit into representations of the enhanced global symmetry F∞ and as a result we expect two types of instanton operators as generators of the ring. Introduce the notion of a balanced node by setting the number of its flavors to equal twice its rank; the subset of balanced nodes forms the Dynkin diagram of the non Abelian factor of the global symmetry on the Coulomb branch.

Objectives

Results

Conclusion