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Argyres-Douglas Theories and S-Duality

Matthew Buican, Simone Giacomelli, Takahiro Nishinaka, Constantinos Papageorgakis

TL;DR

This paper extends the notion of S-duality to N=2 SCFTs with non-integer Coulomb branch dimensions by constructing minimal, well-controlled examples through weak gauging of AD building blocks. Using Hitchin system/class S technology and Seiberg–Witten curves, the authors identify two key rank-3 and rank-4 theories, T_{2,{3ackslash 2},{3ackslash 2}} and T_{3,2,{3ackslash 2},{3ackslash 2}}, which exhibit novel dual frames where fractional-dimension sectors are coupled via weak gauge groups. They demonstrate, via invariant data matching, SW curve analyses, and 3d mirrors, that these theories realize minimal generalizations of Seiberg–Witten and Argyres–Seiberg dualities, including an SU(2) cusp with two I_{3,3} sectors and an exotic rank-two sector, as well as an SU(3) cusp with two I_{3,3} sectors. The work reveals Spin(8)-like triality-inspired actions on coupling parameters and mass parameters in fractional-dimension settings, and establishes UV completions via linear quivers, highlighting rich duality structures on conformal manifolds beyond integer-dimension theories.

Abstract

We generalize S-duality to N=2 superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory with four fundamental flavors by Seiberg and Witten and in SU(3) gauge theory with six fundamental flavors by Argyres and Seiberg. Our constructions start by weakly gauging diagonal SU(2) and SU(3) flavor symmetry subgroups of two copies of a particular rank-one Argyres-Douglas theory (along with sufficient numbers of hypermultiplets to guarantee conformality of the gauging). As we explore the resulting conformal manifold of the SU(2) SCFT, we find an action of S-duality on the parameters of the theory that is reminiscent of Spin(8) triality. On the other hand, as we explore the conformal manifold of the SU(3) theory, we find that an exotic rank-two SCFT emerges in a dual SU(2) description.

Argyres-Douglas Theories and S-Duality

TL;DR

This paper extends the notion of S-duality to N=2 SCFTs with non-integer Coulomb branch dimensions by constructing minimal, well-controlled examples through weak gauging of AD building blocks. Using Hitchin system/class S technology and Seiberg–Witten curves, the authors identify two key rank-3 and rank-4 theories, T_{2,{3ackslash 2},{3ackslash 2}} and T_{3,2,{3ackslash 2},{3ackslash 2}}, which exhibit novel dual frames where fractional-dimension sectors are coupled via weak gauge groups. They demonstrate, via invariant data matching, SW curve analyses, and 3d mirrors, that these theories realize minimal generalizations of Seiberg–Witten and Argyres–Seiberg dualities, including an SU(2) cusp with two I_{3,3} sectors and an exotic rank-two sector, as well as an SU(3) cusp with two I_{3,3} sectors. The work reveals Spin(8)-like triality-inspired actions on coupling parameters and mass parameters in fractional-dimension settings, and establishes UV completions via linear quivers, highlighting rich duality structures on conformal manifolds beyond integer-dimension theories.

Abstract

We generalize S-duality to N=2 superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory with four fundamental flavors by Seiberg and Witten and in SU(3) gauge theory with six fundamental flavors by Argyres and Seiberg. Our constructions start by weakly gauging diagonal SU(2) and SU(3) flavor symmetry subgroups of two copies of a particular rank-one Argyres-Douglas theory (along with sufficient numbers of hypermultiplets to guarantee conformality of the gauging). As we explore the resulting conformal manifold of the SU(2) SCFT, we find an action of S-duality on the parameters of the theory that is reminiscent of Spin(8) triality. On the other hand, as we explore the conformal manifold of the SU(3) theory, we find that an exotic rank-two SCFT emerges in a dual SU(2) description.

Paper Structure

This paper contains 40 sections, 122 equations, 4 figures.

Table of Contents

  1. Introduction and Summary
  2. Introduction and Summary
  3. The Strategy
  4. The Strategy
  5. A minimal generalization of Seiberg and Witten's $S$-duality
  6. A minimal generalization of Seiberg and Witten's $S$-duality
  7. Evidence that $\mathcal{T}_{2,{3\over2},{3\over2}}=I_{4,4}$, and a check of potential cusps
  8. Evidence that $\mathcal{T}_{2,{3\over2},{3\over2}}=I_{4,4}$, and a check of potential cusps
  9. Analysis of the SW curve
  10. Analysis of the SW curve
  11. Cusp at $q = \infty$
  12. Cusps at $q = \pm 2$
  13. The linear quiver
  14. The linear quiver
  15. A minimal generalization of Argyres and Seiberg's $S$-duality
  16. ...and 25 more sections

Figures (4)

  • Figure 1: A UV linear quiver embedding of the $\mathcal{T}_{2,{3\over2},{3\over2}}$ theory.
  • Figure 2: The quiver diagram describing the $III_{6,6}^{3\times[2,2,1,1]}$ theory at $q\sim 0$. The $U(3)$ flavor symmetry naturally appears from the three fundamental hypermultiplets.
  • Figure 3: The quiver diagram describing the $III_{6,6}^{3\times [2,2,1,1]}$ theory at $q\sim 1$. The manifest flavor symmetry is $SU(3) \times U(1)$; the $SU(3)$ comes from $\mathcal{T}_{3,{3\over2}}=III_{6,6}^{2\times [2,2,2],[2,2,1,1]}$, and the $U(1)$ comes from $I_{3,3}$.
  • Figure 4: A UV linear quiver embedding of the $\mathcal{T}_{3,2,{3\over2},{3\over2}}$ theory.