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N=1 dynamics with T_N theory

Kazunobu Maruyoshi, Yuji Tachikawa, Wenbin Yan, Kazuya Yonekura

TL;DR

This article explores ${\cal N}=1$ dynamics arising from coupling the non-Lagrangian ${\cal T}_N$ theory to ${\rm SU}(N)$ gauge groups and fundamental matter, revealing deformation of the moduli space, a dynamical superpotential, and ${\cal N}=1$ Seiberg-Witten curves for Coulomb branches. The authors develop a detailed chiral-ring analysis of the ${\cal T}_N$ sector, derive quantum-moduli constraints via dual quivers and anomaly matching, and show how Higgsing procedures reproduce familiar SQCD limits. They extend the framework to include one extra flavor, additional ${\rm SU}(N)$ gaugings, and general quiver-like graphs, obtaining corresponding holomorphic curves and spectra that generalize Seiberg-Witten-type dynamics to non-Lagrangian building blocks. The results establish a coherent holomorphy-driven approach to a broad class of ${\cal N}=1$ theories built from ${\cal T}_N$ blocks, with potential M5-brane (6d) realizations and implications for non-conventional dualities and duality webs.

Abstract

We study the dynamics of N=1 supersymmetric systems consisting of the strongly-coupled superconformal theory T_N, SU(N) gauge groups, and fundamental chiral multiplets. We demonstrate that such systems exhibit familiar phenomena such as deformation of the vacuum moduli space, appearance of the dynamical superpotential, and Coulomb branches with N=1 Seiberg-Witten curves. The analysis requires a rather detailed knowledge of the chiral ring of the T_N theory, which will also be discussed at length.

N=1 dynamics with T_N theory

TL;DR

This article explores dynamics arising from coupling the non-Lagrangian theory to gauge groups and fundamental matter, revealing deformation of the moduli space, a dynamical superpotential, and Seiberg-Witten curves for Coulomb branches. The authors develop a detailed chiral-ring analysis of the sector, derive quantum-moduli constraints via dual quivers and anomaly matching, and show how Higgsing procedures reproduce familiar SQCD limits. They extend the framework to include one extra flavor, additional gaugings, and general quiver-like graphs, obtaining corresponding holomorphic curves and spectra that generalize Seiberg-Witten-type dynamics to non-Lagrangian building blocks. The results establish a coherent holomorphy-driven approach to a broad class of theories built from blocks, with potential M5-brane (6d) realizations and implications for non-conventional dualities and duality webs.

Abstract

We study the dynamics of N=1 supersymmetric systems consisting of the strongly-coupled superconformal theory T_N, SU(N) gauge groups, and fundamental chiral multiplets. We demonstrate that such systems exhibit familiar phenomena such as deformation of the vacuum moduli space, appearance of the dynamical superpotential, and Coulomb branches with N=1 Seiberg-Witten curves. The analysis requires a rather detailed knowledge of the chiral ring of the T_N theory, which will also be discussed at length.

Paper Structure

This paper contains 30 sections, 74 equations, 2 figures.

Table of Contents

  1. Introduction and summary
  2. The chiral ring of $T_N$ theory
  3. Summary of chiral operators
  4. Summary of chiral ring relations
  5. Derivation of chiral ring relations
  6. The relations on $\mathop{\rm tr} \mu^k$:
  7. The relations on $\mu Q$:
  8. The relation on $QQ$ :
  9. The relations relating $Q_{i_Ai_Bi_C}$ and $Q^{i_Ai_Bi_C}$:
  10. Chiral rings from superconformal index
  11. Deformed moduli space
  12. Statement of the result
  13. Higgsing from $\mathop{\rm SU}(N)$ to $\mathop{\rm SU}(N-1)$
  14. Check of the anomaly
  15. Higgsing to SQCD and others
  16. ...and 15 more sections

Figures (2)

  • Figure 1: An example of generalized models.
  • Figure 2: A genus-zero graph. A genus-one graph can be obtained by gauging the diagonal subgroup of $\mathop{\rm SU}(N)_{n+1}$ and $\mathop{\rm SU}(N)_{2n+1}$.