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Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs

Emanuele Beratto, Noppadol Mekareeya, Matteo Sacchi

TL;DR

This work analyzes exactly marginal deformations in 3d ${ m S}$-fold SCFTs, focusing on ${ m N}=2$ preserving operators and the fate of supersymmetry in the IR. Using two constructions—gaugings of the diagonal flavor of ${T(U(N))}$ and of ${T^{[2,1^2]}_{[2,1^2]}(SU(4))}$—the authors compute and interpret superconformal indices to identify extra SUSY currents and hence SUSY enhancement patterns. They find robust ${ m N}=4$ enhancement across many CS-level and flavor configurations for the ${T(U(N))}$-based theories, with subtleties arising from monopole sectors (notably at ${k=2}$ and ${k= rac{1}{2}}$-like regimes) and from special cases yielding ${ m N}=3$ or higher, including instances suggesting ${ m N}=5$ in certain setups. Extending to the ${T^{[2,1^2]}_{[2,1^2]}(SU(4))}$ building block, preliminary results indicate a more intricate spectrum of marginal operators and monopole relations, underscoring the richer structure and challenges in fully classifying SUSY enhancements in these models. The work thus advances the understanding of conformal manifolds and SUSY enhancement in 3d ${ m S}$-fold theories, with implications for dualities and IR dynamics in lower-dimensional SCFTs. $

Abstract

The study of exactly marginal deformations of superconformal field theories is a topic that has received considerable attention due to their rich properties. We investigate the $\mathcal{N}=2$ preserving exactly marginal operators of 3d $S$-fold SCFTs. Two families of such theories are considered: one is constructed by gauging the diagonal flavour symmetry of the $T(U(2))$ and $T(U(3))$ theories, and the other by gauging the diagonal flavour symmetry of the $T^{[2,1^2]}_{[2,1^2]}(SU(4))$ theory. In both families, it is possible to turn on a Chern--Simons level for each gauge group and to couple to each theory various numbers of hypermultiplets. The detailed analysis of the exactly marginal operators, along with the superconformal indices, allows us to determine whether supersymmetry gets enhanced in the infrared and to deduce the amount of supersymmetry of the corresponding SCFT.

Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs

TL;DR

This work analyzes exactly marginal deformations in 3d -fold SCFTs, focusing on preserving operators and the fate of supersymmetry in the IR. Using two constructions—gaugings of the diagonal flavor of and of —the authors compute and interpret superconformal indices to identify extra SUSY currents and hence SUSY enhancement patterns. They find robust enhancement across many CS-level and flavor configurations for the -based theories, with subtleties arising from monopole sectors (notably at and -like regimes) and from special cases yielding or higher, including instances suggesting in certain setups. Extending to the building block, preliminary results indicate a more intricate spectrum of marginal operators and monopole relations, underscoring the richer structure and challenges in fully classifying SUSY enhancements in these models. The work thus advances the understanding of conformal manifolds and SUSY enhancement in 3d -fold theories, with implications for dualities and IR dynamics in lower-dimensional SCFTs. $

Abstract

The study of exactly marginal deformations of superconformal field theories is a topic that has received considerable attention due to their rich properties. We investigate the preserving exactly marginal operators of 3d -fold SCFTs. Two families of such theories are considered: one is constructed by gauging the diagonal flavour symmetry of the and theories, and the other by gauging the diagonal flavour symmetry of the theory. In both families, it is possible to turn on a Chern--Simons level for each gauge group and to couple to each theory various numbers of hypermultiplets. The detailed analysis of the exactly marginal operators, along with the superconformal indices, allows us to determine whether supersymmetry gets enhanced in the infrared and to deduce the amount of supersymmetry of the corresponding SCFT.

Paper Structure

This paper contains 30 sections, 228 equations.

Table of Contents

  1. Introduction and conclusion
  2. $S$-fold theories with the $T(U(N))$ building block
  3. The $T(U(N))$ theory
  4. $U(N)_k$ gauge group and zero flavour
  5. $U(N)_k$ gauge group with $k\neq0$ and $n \geq 1$ flavours
  6. The case of $|k| \geq 3$, with $n \geq 1$
  7. The case of $k=2$ and $n\geq 2$
  8. The case of $k=2$ and $n=1$
  9. Comments on the case of $k=-2$
  10. The case of $k=1$ and $n=1$
  11. $U(N)_0$ gauge group and $n$ flavour
  12. $S$-fold theories with the $T^{[2,1^2]}_{[2,1^2]} (SU(4))$ building block: Preliminary results
  13. The $T^{[2,1^2]}_{[2,1^2]}(SU(4))$ theory
  14. $U(2)_k$ gauge group with zero flavour
  15. The case of $|k| \geq 3$
  16. ...and 15 more sections