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A tale of exceptional 3d dualities

Sergio Benvenuti

Abstract

We consider interesting Seiberg dualities for $Usp$ gauge theories with an antisymmetric, $8$ fundamentals and no superpotential. We reduce to three dimensions and systematically analyze deformations triggered by real and complex masses, reaching a plethora of $\mathcal{N}\!=\!2$ dualities for $U(N)$ and $Usp(2N)$ gauge theories, possibly with monopole superpotentials and Chern-Simons interactions. Special cases of these "exceptional dualities" are: supersymmetry enhancement dualities, "duality appetizers" and many known dualities relating rank-$1$ gauge groups. The $4d$ $\mathcal{N}\!=\!1$ $Usp$ dualities provide a unified perspective on many curious phenomena of $3d$ and $4d$ gauge theories with four supercharges. Finally, we propose a free mirror for $A_{2N}$ Argyres-Douglas, with its related adjoint-$Usp(2N)$ duality, and we construct a mirror for adjoint-$U(N)$, with an arbitrary number flavors and zero superpotential.

A tale of exceptional 3d dualities

Abstract

We consider interesting Seiberg dualities for gauge theories with an antisymmetric, fundamentals and no superpotential. We reduce to three dimensions and systematically analyze deformations triggered by real and complex masses, reaching a plethora of dualities for and gauge theories, possibly with monopole superpotentials and Chern-Simons interactions. Special cases of these "exceptional dualities" are: supersymmetry enhancement dualities, "duality appetizers" and many known dualities relating rank- gauge groups. The dualities provide a unified perspective on many curious phenomena of and gauge theories with four supercharges. Finally, we propose a free mirror for Argyres-Douglas, with its related adjoint- duality, and we construct a mirror for adjoint-, with an arbitrary number flavors and zero superpotential.

Paper Structure

This paper contains 29 sections, 98 equations.

Table of Contents

  1. Introduction and summary
  2. Note.
  3. Vector-like real masses: self-dualities without Chern-Simons
  4. $Usp(2N_c)$ with $8$ flavors, ${\mathcal{W}}={\mathfrak M}$
  5. $Usp(2N_c)$ with $6$ flavors, ${\mathcal{W}}=0$
  6. $U(N_c)$ with $4$ flavors, ${\mathcal{W}}={\mathfrak M}^++{\mathfrak M}^-$
  7. $U(N_c)$ with $3$ flavors, ${\mathcal{W}}={\mathfrak M}^+$
  8. $U(N_c)$ with $2$ flavors, ${\mathcal{W}}=0$
  9. A mirror like duality and its brane setup
  10. Brane interpretation
  11. Turning on a complex mass: cubic Wess-Zumino duals
  12. $U(N_c)$ with $3$ flavors, ${\mathcal{W}}={\mathfrak M}^++{\mathfrak M}^-$
  13. Decoupling of the tower $\mu_{44; r}$.
  14. The most general superpotential.
  15. Confining duality.
  16. ...and 14 more sections