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Refined Checks and Exact Dualities in Three Dimensions

Prarit Agarwal, Antonio Amariti, Massimo Siani

TL;DR

The paper analyzes three-dimensional dualities across unitary, orthogonal, and symplectic gauge groups by computing and exactly matching partition functions on the squashed sphere $S^3_b$, for arbitrary ranks and Chern-Simons levels. It develops and tests a comprehensive framework for necklace quivers with orientifold projections and for theories with tensor matter that have free duals, using localization to hyperbolic gamma-function matrix models and rigorous finite-$N$ checks. A key contribution is a prescription for incorporating IR accidental symmetry mixing into $R$-charge extremization, enabling consistent dual descriptions even when some operators decouple as free fields. The results deliver strong, nonperturbative evidence for a wide web of 3d dualities and clarify how accidental symmetries affect $F$-maximization and dual maps, with concrete examples including ABJM-like quivers and adjoint/tensor matter cases, shedding light on IR dynamics and potential $F$-theorem implications.

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.

Refined Checks and Exact Dualities in Three Dimensions

TL;DR

The paper analyzes three-dimensional dualities across unitary, orthogonal, and symplectic gauge groups by computing and exactly matching partition functions on the squashed sphere , for arbitrary ranks and Chern-Simons levels. It develops and tests a comprehensive framework for necklace quivers with orientifold projections and for theories with tensor matter that have free duals, using localization to hyperbolic gamma-function matrix models and rigorous finite- checks. A key contribution is a prescription for incorporating IR accidental symmetry mixing into -charge extremization, enabling consistent dual descriptions even when some operators decouple as free fields. The results deliver strong, nonperturbative evidence for a wide web of 3d dualities and clarify how accidental symmetries affect -maximization and dual maps, with concrete examples including ABJM-like quivers and adjoint/tensor matter cases, shedding light on IR dynamics and potential -theorem implications.

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.

Paper Structure

This paper contains 27 sections, 90 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The partition function on a squashed three sphere
  3. Hyperbolic functions
  4. Families of quiver gauge theories and M$2$ branes
  5. Unitary groups
  6. Duality
  7. Orthogonal and symplectic groups: the orientifold
  8. Duality
  9. Exact results for the dualities
  10. Duality in $U(N)_k$ non-chiral quivers
  11. Adding an adjoint field
  12. The first class of orientilfolds: O$3$ planes
  13. Duality on an $SP(2N)_k$ node
  14. Duality on an $SO(2N)_{2k}$ node
  15. The second class of orientifolds: duality on $SO(2N+1)_k$
  16. ...and 12 more sections

Figures (3)

  • Figure 1: A type IIB embedding of orthogonal and symplectic field theories via O$3^{\pm}$ planes on a stack of D$3$.
  • Figure 2: Dual phases describing a stack of M$2$ branes probing a Calabi-Yau fourfold.
  • Figure 3: Dual phases describing a stack of M$2$ branes probing Calabi-Yau fourfold with adjoint matter involved in the duality.