A Duality Web in Condensed Matter Systems

TL;DR

This paper explores a web of dualities in condensed matter physics, deriving three-dimensional dualities from a conjecture relating Dirac fermions and scalar theories, and extends the discussion to finite temperatures and higher dimensions.

Contribution

It introduces a novel duality web in condensed matter systems, connecting Dirac fermions, scalar theories, and higher-dimensional bulk-boundary theories, including effects of holonomy and temperature.

Findings

Dualities are unaffected by non-trivial holonomy.

Mean-field methods effectively study dualities at finite temperature.

Constraints on duality webs in higher dimensions are identified.

Abstract

We study various dualities in condensed matter systems. The dualities in three dimensions could be derived from a conjecture of a duality between a Dirac fermion theory and an interacting scalar field theory at the Wilson-Fisher fixed point and zero temperature in three dimensions. We show that the dualities are not affected by the non-trivial holonomy, use a mean-field method to study, and discuss the dualities at a finite temperature. Finally, we combine a bulk theory, which is an Abelian $p$-form theory with a theta term in $2p+2$ dimensions, and a boundary theory, which is a $2p+1$ dimensional theory, to discuss constraints and difficulties of a duality web in $2p+1$ dimensions.