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N=2 S-duality Revisited

Matthew Buican, Zoltan Laczko, Takahiro Nishinaka

TL;DR

This work identifies a minimal Argyres-Douglas S-duality setup in which the exotic T_{3,{3\over2}} theory factorizes into a free hypermultiplet and an interacting TX sector. Using chiral algebra bootstrap, the authors determine chi(TX) and its vacuum character via AKM representations, enabling a precise 4D/2D link to the Schur index of TX. They conjecture a compact, consistent chiral algebra for TX built from a Virasoro stress tensor at c_{2d}=-26, AKM currents at critical levels, and a single h=\tfrac{3}{2} AKM primary W_{aI}, and they bootstrap its OPEs to verify closure and null relations. The TX Schur index is expressed in AKM characters, revealing connections to T_N structures and enabling checks against Hall-Littlewood data and the S^3 partition function through a small S^1 reduction, with Witten anomalies offering intriguing constraints on 2D/4D correspondences.

Abstract

Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), $T_{3,{3\over2}}$, emerging in this duality splits into a free piece and an interacting piece, T_X, even though this factorization seems invisible in the Seiberg-Witten (SW) curve derived from the corresponding M5-brane construction. Without a Lagrangian, an associated topological field theory, a BPS spectrum, or even an SW curve, we nonetheless obtain exact information about T_X by bootstrapping its chiral algebra, chi(T_X), and finding the corresponding vacuum character in terms of Affine Kac-Moody characters. By a standard 4D/2D correspondence, this result gives us the Schur index for T_X and, by studying this quantity in the limit of small S^1, we make contact with a proposed S^1 reduction. Along the way, we discuss various properties of T_X: as an N=1 theory, it has flavor symmetry SU(3)XSU(2)XU(1), the central charge of chi(T_X) matches the central charge of the bc ghosts in bosonic string theory, and its global SU(2) symmetry has a Witten anomaly. This anomaly does not prevent us from building conformal manifolds out of arbitrary numbers of T_X theories (giving us a surprisingly close AD relative of Gaiotto's T_N theories), but it does lead to some open questions in the context of the chiral algebra / 4D N=2 SCFT correspondence.

N=2 S-duality Revisited

TL;DR

This work identifies a minimal Argyres-Douglas S-duality setup in which the exotic T_{3,{3\over2}} theory factorizes into a free hypermultiplet and an interacting TX sector. Using chiral algebra bootstrap, the authors determine chi(TX) and its vacuum character via AKM representations, enabling a precise 4D/2D link to the Schur index of TX. They conjecture a compact, consistent chiral algebra for TX built from a Virasoro stress tensor at c_{2d}=-26, AKM currents at critical levels, and a single h=\tfrac{3}{2} AKM primary W_{aI}, and they bootstrap its OPEs to verify closure and null relations. The TX Schur index is expressed in AKM characters, revealing connections to T_N structures and enabling checks against Hall-Littlewood data and the S^3 partition function through a small S^1 reduction, with Witten anomalies offering intriguing constraints on 2D/4D correspondences.

Abstract

Using the chiral algebra bootstrap, we revisit the simplest Argyres-Douglas (AD) generalization of Argyres-Seiberg S-duality. We argue that the exotic AD superconformal field theory (SCFT), , emerging in this duality splits into a free piece and an interacting piece, T_X, even though this factorization seems invisible in the Seiberg-Witten (SW) curve derived from the corresponding M5-brane construction. Without a Lagrangian, an associated topological field theory, a BPS spectrum, or even an SW curve, we nonetheless obtain exact information about T_X by bootstrapping its chiral algebra, chi(T_X), and finding the corresponding vacuum character in terms of Affine Kac-Moody characters. By a standard 4D/2D correspondence, this result gives us the Schur index for T_X and, by studying this quantity in the limit of small S^1, we make contact with a proposed S^1 reduction. Along the way, we discuss various properties of T_X: as an N=1 theory, it has flavor symmetry SU(3)XSU(2)XU(1), the central charge of chi(T_X) matches the central charge of the bc ghosts in bosonic string theory, and its global SU(2) symmetry has a Witten anomaly. This anomaly does not prevent us from building conformal manifolds out of arbitrary numbers of T_X theories (giving us a surprisingly close AD relative of Gaiotto's T_N theories), but it does lead to some open questions in the context of the chiral algebra / 4D N=2 SCFT correspondence.

Paper Structure

This paper contains 25 sections, 94 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Introduction
  3. The Schur sector and the 4D/2D correspondence
  4. The Schur sector and the 4D/2D correspondence
  5. A chiral algebra argument for $\mathcal{T}_{3,{3\over2}}=\mathcal{T}_X\oplus {\rm hyper}$
  6. A chiral algebra argument for $\mathcal{T}_{3,{3\over2}}=\mathcal{T}_X\oplus {\rm hyper}$
  7. The Schur index of $\mathcal{T}_X$ from $S$-duality and inversion
  8. The Schur index of $\mathcal{T}_X$ from $S$-duality and inversion
  9. A chiral algebra conjecture
  10. A chiral algebra conjecture
  11. Bootstrapping the Chiral Algebra of $\mathcal{T}_X$
  12. Bootstrapping the Chiral Algebra of $\mathcal{T}_X$
  13. Re-writing the index in terms of AKM characters
  14. Re-writing the index in terms of AKM characters
  15. A remark on the Hall-Littlewood chiral ring of $\mathcal{T}_X$ and the Schur sector
  16. ...and 10 more sections

Figures (6)

  • Figure 1: The quiver diagram describing the simplest (i.e., lowest rank) AD generalization of Argyres-Seiberg duality in the $SU(3)$ duality frame. The total flavor symmetry is $U(3)$. In Buican:2014hfa, this theory was called the '' $\mathcal{T}_{3,2,{3\over2},{3\over2}}$" SCFT.
  • Figure 2: The quiver diagram describing the theory dual to the one in Fig. \ref{['quiver1']}. The $SU(3)\subset U(3)$ symmetry is furnished by the $\mathcal{T}_{3,{3\over2}}$ theory while the $U(1)\subset U(3)$ symmetry is furnished by the $(A_1, D_4)$ SCFT. In Buican:2014hfa, this theory was called the '' $\mathcal{T}_{3,2,{3\over2},{3\over2}}$" SCFT.
  • Figure 3: The quiver diagram describing the mirror of the $S^1$ reduction of $\mathcal{T}_{3,{3\over2}}$.
  • Figure 4: The factorized form of the $\mathcal{T}_{3,{3\over2}}$ SCFT into a decoupled free hypermultiplet and the interacting $\mathcal{T}_X$ SCFT.
  • Figure 5: The above SCFT is inconsistent because of the $SU(2)$ anomaly of the $\mathcal{T}_X$ theory. It would be interesting to study how this inconsistency is manifested in the chiral algebra setting.
  • ...and 1 more figures