A 4D duality web

TL;DR

This paper constructs a web of non-supersymmetric dualities in four dimensions involving theta and Maxwell terms, extending known 3D dualities and suggesting connections across multiple dimensions with potential applications to topological insulators.

Contribution

It introduces a novel 4D duality web based on bosonization, mirroring 3D dualities, and extends the understanding of dualities across different spacetime dimensions.

Findings

Constructed a 4D duality web with boson-boson, fermion-fermion, and boson-fermion dualities.

Extended the 3D duality framework to four dimensions using an analog of the massive construction.

Proposed a connection between low energy theories across 4D, 3D, and 2D, with implications for topological insulators.

Abstract

We construct a web of non-supersymmetric dualities in four spacetime dimensions for theories with theta and Maxwell terms. Our construction mirrors the recipe used in (2+1)-dimensions to demonstrate a similar duality for theories with Chern-Simons terms. As in the 3-dimensional case, the web consists of boson-boson, fermion-fermion and boson-fermion dualities, any one of which can be taken as a seed for the remaining two. To be concrete, we begin by constructing the basic bosonization duality which we then use to generate the web, using an analog of the 3-dimensional massive construction given in \cite{Nastase:2017gxr} . The resulting 4-dimensional duality web is best understood as an extension of the, by now well-known, 3-dimensional case due to its somewhat singular nature. We conjecture that this is the final thread in a multi-dimensional duality web that connects low energy theories in 4-, 3- and 2-spacetime dimensions and speculate on its application to 3-dimensional topological insulators.