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$(0, 4)$ dualities

Pavel Putrov, Jaewon Song, Wenbin Yan

TL;DR

The paper develops a 2d ${\cal N}=(0,4)$ framework mirroring 4d class ${\cal S}$ dualities, showing that a wide class of quiver gauge theories flow to SCFTs whose spectra are organized by a 2d TQFT on a Riemann surface ${\cal C}$. It provides explicit index computations for SU(2) and SU(N) quivers, unveils a 2d analogue of the $T_N$ sector via ${\cal T}_N^{(0,4)}$ and Argyres–Seiberg-type dualities, and demonstrates LG dual descriptions and $(0,2)$/$(2,2)$ analogues of crossing symmetry. The results connect 2d SCFTs to higher-dimensional constructions, including compactifications of the 6d ${\cal N}=(2,0)$ theory on ${\mathbb{CP}}^1 \times {\cal C}$, and suggest a reduction of Vafa–Witten TQFT structure to 2d, with implications for non-Lagrangian Higgs branches (e.g., $E_6$) and duality webs. Overall, the work extends the class ${\cal S}$ paradigm to two dimensions, providing new exact results and a unifying TQFT interpretation for a broad family of ${\cal N}=(0,4)$ theories.

Abstract

We study a class of two-dimensional ${\cal N}=(0, 4)$ quiver gauge theories that flow to superconformal field theories. We find dualities for the superconformal field theories similar to the 4d ${\cal N}=2$ theories of class ${\cal S}$, labelled by a Riemann surface ${\cal C}$. The dual descriptions arise from various pair-of-pants decompositions, that involves an analog of the $T_N$ theory. Especially, we find the superconformal index of such theories can be written in terms of a topological field theory on ${\cal C}$. We interpret this class of SCFTs as the ones coming from compactifying 6d ${\cal N}=(2, 0)$ theory on $\mathbb{CP}^1 \times {\cal C}$

$(0, 4)$ dualities

TL;DR

The paper develops a 2d framework mirroring 4d class dualities, showing that a wide class of quiver gauge theories flow to SCFTs whose spectra are organized by a 2d TQFT on a Riemann surface . It provides explicit index computations for SU(2) and SU(N) quivers, unveils a 2d analogue of the sector via and Argyres–Seiberg-type dualities, and demonstrates LG dual descriptions and / analogues of crossing symmetry. The results connect 2d SCFTs to higher-dimensional constructions, including compactifications of the 6d theory on , and suggest a reduction of Vafa–Witten TQFT structure to 2d, with implications for non-Lagrangian Higgs branches (e.g., ) and duality webs. Overall, the work extends the class paradigm to two dimensions, providing new exact results and a unifying TQFT interpretation for a broad family of theories.

Abstract

We study a class of two-dimensional quiver gauge theories that flow to superconformal field theories. We find dualities for the superconformal field theories similar to the 4d theories of class , labelled by a Riemann surface . The dual descriptions arise from various pair-of-pants decompositions, that involves an analog of the theory. Especially, we find the superconformal index of such theories can be written in terms of a topological field theory on . We interpret this class of SCFTs as the ones coming from compactifying 6d theory on

Paper Structure

This paper contains 30 sections, 4 theorems, 132 equations, 12 figures, 6 tables.

Table of Contents

  1. Introduction and summary
  2. Dualities of $SU(2)$ generalized quiver
  3. $SU(2)$ with 4 flavors and its crossing symmetry
  4. Dualities of quiver theories and the TQFT structure of the index
  5. Elliptic genus and 2d TQFT
  6. Dualities between generalized quiver theories
  7. Duality to a Landau-Ginzburg model
  8. ${\cal N}=(4, 4)$ theories
  9. $SU(N)$ theories
  10. $SU(N)$ with $2N$ flavors and its crossing symmetry
  11. Dualities of quiver theories and $T_N^{(0, 4)}$ theory
  12. Quiver gauge theories
  13. Linear quiver
  14. Circular quiver
  15. Analog of Argyres-Seiberg duality and $T^{(0, 4)}_3$ theory
  16. ...and 15 more sections

Key Result

Proposition 1

If $f\in {\cal H}^{(m)}_{SU(2)},\;m>0$ has no poles, it is zero.

Figures (12)

  • Figure 1: The quiver notations for: a) theory $T_2^{(0,4)}$ of 8 chiral multiplets in tri-fundamental representation of $SU(2)^3$ flavor symmetry, b) $(0,4)$$SU(2)$ vector multiplet.
  • Figure 2: The quiver notation for the theory obtained by gauging the diagonal subgroup of two $SU(2)$ flavor symmetries from two different copies of $T_2^{(0,4)}$ with $(0,4)$$SU(2)$ vector multiplet.
  • Figure 3: The symmetry under exchange of $SU(2)$ factors in the flavor symmetry of the theory can be interpreted as the crossing symmetry of the quiver diagram. The letters $x,y,z,w$ used to distinguish various $SU(2)$ factors and later in the text denote the corresponding $SU(2)$ flavor fugacities in the elliptic genus.
  • Figure 4: Duality between two different $(0,4)$ theories with $SU(2)^3$ gauge group and $SU(2)^6$ flavor symmetry. For the sake of simplicity we suppress $SU(2)$ inscribed inside squares and circles of the quivers.
  • Figure 5: Duality between two different $(0,4)$ theories with $SU(2)^3$ gauge group.
  • ...and 7 more figures

Theorems & Definitions (8)

  • Definition 1
  • Proposition 1
  • proof
  • Proposition 2
  • Lemma 3
  • proof
  • Theorem 1
  • proof