An E7 Surprise

TL;DR

The paper investigates how Seiberg duality in SU(2) with N_f=4 SQCD can reveal an enhanced E7 flavor symmetry. It constructs two complementary setups—the doubled theory $\,\mathcal{T}_{II}$ and a 4d-5d boundary condition $\,\mathcal{B}_{\mathcal{T}}$ attached to 28 hypermultiplets—that realize an apparent E7 symmetry in their indices and operator spectra. Through index identities and operator counting, it provides evidence for a special point in the exactly marginal deformation space where the flavor symmetry genuinely enhances to E7, and it demonstrates a consistent dimensional reduction to a 3d context where an SO(12) symmetry emerges on a boundary. The work thus illuminates a novel route to hidden symmetry and duality networks, with concrete checks via sphere indices, half-indices, and partition functions, and connects 4d-5d-3d perspectives across dimensionful boundaries.

Abstract

We explore some curious implications of Seiberg duality for an SU(2) four-dimensional gauge theory with eight chiral doublets. We argue that two copies of the theory can be deformed by an exactly marginal quartic superpotential so that they acquire an enhanced E7 flavor symmetry. We argue that a single copy of the theory can be used to define an E7-invariant superconformal boundary condition for a theory of 28 five-dimensional free hypermultiplets. Finally, we derive similar statements for three-dimensional gauge theories such as an SU(2) gauge theory with six chiral doublets or Nf=4 SQED.