Dualities from dualities: the sequential deconfinement technique

TL;DR

This paper explores a method called sequential deconfinement to derive complex dualities in supersymmetric quantum field theories, revealing new dualities and symmetry enhancements through iterative elementary dualities.

Contribution

It introduces the sequential deconfinement technique for deriving dualities in theories with tensor matter, including a new self-duality with E6 symmetry enhancement.

Findings

Derived new dual descriptions of supersymmetric theories.

Established connections between dualities and hypergeometric integral identities.

Discovered a novel self-duality with E6 symmetry enhancement.

Abstract

It is an interesting question whether a given infra-red duality between quantum field theories can be explained in terms of other more elementary dualities. For example recently it has been shown that mirror dualities can be obtained by iterative applications of Seiberg-like dualities. In this paper we continue this line of investigation focusing on theories with tensor matter. In such cases one can apply the idea of deconfinement, which consists of trading the tensor matter for extra gauge nodes by means of a suitable elementary duality. This gives an auxiliary dual frame which can then be manipulated with further dualizations, in an iterative procedure eventually yielding an interesting dual description of the original theory. The sequential deconfinement technique has avatars in different areas of mathematical physics, such as the study of hypergeometric and elliptic hypergeometric integral identities or of $2d$ free field correlators. We discuss various examples in the context $4d$ $\mathcal{N}=1$ supersymmetric theories, which are related to elliptic hypergeometric integrals. These include a new self-duality involving a quiver theory which exhibits a non-trivial global symmetry enhancement to $E_6$.