Refined Checks and Exact Dualities in Three Dimensions

TL;DR

This paper provides evidence for a broad class of dualities in three-dimensional gauge theories by matching partition functions, focusing on necklace quiver models and theories with tensor matter fields, including effects of R-symmetry mixing.

Contribution

It introduces a comprehensive method to verify dualities in 3D gauge theories through exact partition function matching, including cases with R-symmetry mixing and orientifold projections.

Findings

Partition functions match for dual phases across various models.

Dualities hold for necklace quiver theories with orthogonal and symplectic groups.

Inclusion of R-symmetry mixing improves duality verification.

Abstract

We discuss and provide nontrivial evidence for a large class of dualities in three-dimensional field theories with different gauge groups. We match the full partition functions of the dual phases for any value of the couplings to underpin our proposals. We focus on two classes of models. The first class, motivated by the AdS/CFT conjecture, consists of necklace U(N) quiver gauge theories with non chiral matter fields. We also consider orientifold projections and establish dualities among necklace quivers with alternating orthogonal and symplectic groups. The second class consists of theories with tensor matter fields with free theory duals. In most of these cases the R-symmetry mixes with IR accidental symmetries and we develop the prescription to include their contribution into the partition function and the extremization problem accordingly.