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Comments on 3d Seiberg-like dualities

Francesco Benini, Cyril Closset, Stefano Cremonesi

TL;DR

The paper develops a framework for Seiberg-like dualities in three-dimensional N=2 theories, highlighting the crucial role of global Chern-Simons terms that couple background global symmetries to the dynamics. It constructs new dual pairs for unitary U(n) YM-CS theories with chiral matter via real mass deformations from Aharony duality and extends these ideas to CS quivers, as well as to symplectic and orthogonal groups. The authors test proposals by matching localized S^3_b partition functions and provide insight into RG flows, convergence, and Z-minimization, offering a coherent picture of dualities in 3d gauge theories with complex flavor structures. The results pave the way for applying Seiberg-like dualities to more intricate quivers and for cross-checks with superconformal indices and holographic constructions.

Abstract

We study Seiberg-like dualities in three dimensional N=2 supersymmetric theories, emphasizing Chern-Simons terms for the global symmetry group, which affect contact terms in two-point functions of global currents and are essential to the duality map. We introduce new Seiberg-like dualities for Yang-Mills-Chern-Simons theories with unitary gauge groups with arbitrary numbers of matter fields in the fundamental and antifundamental representations. These dualities are derived from Aharony duality by real mass deformations. They allow to initiate the systematic study of Seiberg-like dualities in Chern-Simons quivers. We also comment on known Seiberg-like dualities for symplectic and orthogonal gauge groups and extend the latter to the Yang-Mills case. We check our proposals by showing that the localized partition functions on the squashed S^3 match between dual descriptions.

Comments on 3d Seiberg-like dualities

TL;DR

The paper develops a framework for Seiberg-like dualities in three-dimensional N=2 theories, highlighting the crucial role of global Chern-Simons terms that couple background global symmetries to the dynamics. It constructs new dual pairs for unitary U(n) YM-CS theories with chiral matter via real mass deformations from Aharony duality and extends these ideas to CS quivers, as well as to symplectic and orthogonal groups. The authors test proposals by matching localized S^3_b partition functions and provide insight into RG flows, convergence, and Z-minimization, offering a coherent picture of dualities in 3d gauge theories with complex flavor structures. The results pave the way for applying Seiberg-like dualities to more intricate quivers and for cross-checks with superconformal indices and holographic constructions.

Abstract

We study Seiberg-like dualities in three dimensional N=2 supersymmetric theories, emphasizing Chern-Simons terms for the global symmetry group, which affect contact terms in two-point functions of global currents and are essential to the duality map. We introduce new Seiberg-like dualities for Yang-Mills-Chern-Simons theories with unitary gauge groups with arbitrary numbers of matter fields in the fundamental and antifundamental representations. These dualities are derived from Aharony duality by real mass deformations. They allow to initiate the systematic study of Seiberg-like dualities in Chern-Simons quivers. We also comment on known Seiberg-like dualities for symplectic and orthogonal gauge groups and extend the latter to the Yang-Mills case. We check our proposals by showing that the localized partition functions on the squashed S^3 match between dual descriptions.

Paper Structure

This paper contains 31 sections, 156 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Global Chern-Simons terms
  3. Dualities for $U(n)$ theories with "chiral" matter
  4. Aharony's duality
  5. Chiral SQCD with Chern-Simons levels
  6. Dual of the $[\bm{p}, \bm{0}]a$ theory
  7. Dual of the $[\bm{p}, \bm{q}]a$ theory
  8. Dual of the $[\bm{p}, \bm{q}]^*a$ theory
  9. Summary of the $U(n)_k$ dualities
  10. Consequences for Chern-Simons quivers
  11. Minimally chiral case
  12. Maximally chiral case
  13. Dualities for $U(n)$ theories and $S^3_b$ partition function
  14. $S^3_b$ partition function for chiral $U(n)$ SQCD
  15. Aharony duality and real mass deformations
  16. ...and 16 more sections

Figures (2)

  • Figure 1: (a) Quiver diagram of the $U(n)_k$ electric theory. (b) Quiver diagram of the magnetic $U(m)_{-k}$ theory, where $m$ is defined in (\ref{['m for various cases']}). For special values of the parameters, there might be extra singlets $T$ and/or $\tilde{T}$ in addition to the mesons $M$, as explained in the text.
  • Figure 2: Seiberg-like duality acting on a quiver. Remark that the dual quiver also contains some mesonic fields $M$, although generally many of the mesons will be massive due to the superpotential.