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Singular points in N=2 SQCD

Simone Giacomelli

TL;DR

This work analyzes singular points in N=2 SQCD with classical gauge groups using the Gaiotto-Seiberg-Tachikawa framework. It shows that at maximally singular points the low-energy theory generically decomposes into two scale-invariant sectors (A and B) connected by an infrared-free SU(2) gauge group, with abelian factors present in certain cases. The A and B sectors are realized as a three-punctured-sphere compactification of a 6d theory and a D-type Argyres-Douglas theory, respectively, and this structure accounts for dualities and the flavor/symmetry properties across SU, USp, and SO theories. Upon soft N=1 perturbations, a finite number of confining vacua remains, tying together confinement dynamics with the underlying Seiberg-Witten geometry and confirming a unified infrared picture for these maximally singular points. The results also recover known special cases like Chebyshev points and connect to 6d constructions, offering a robust framework for exploring broader families of theories and dualities.

Abstract

We revisit the study of singular points in N=2 SQCD with classical gauge groups. Using a technique proposed recently by Gaiotto, Seiberg and Tachikawa we find that the low-energy physics at the maximally singular point involves two superconformal sectors coupled to an infrared free SU(2) gauge group. When one softly breaks extended supersymmetry to N=1 adding a mass term for the chiral multiplet in the adjoint representation, a finite number of vacua remain and the theory becomes confining. Our analysis allows to identify the low-energy physics at these distinguished points in the moduli space. In some cases, which we will describe in detail, two sectors coupled to an infrared free SU(2) gauge group emerge as before. For USp and SO gauge groups one of these sectors is always free, contrary to the SU case.

Singular points in N=2 SQCD

TL;DR

This work analyzes singular points in N=2 SQCD with classical gauge groups using the Gaiotto-Seiberg-Tachikawa framework. It shows that at maximally singular points the low-energy theory generically decomposes into two scale-invariant sectors (A and B) connected by an infrared-free SU(2) gauge group, with abelian factors present in certain cases. The A and B sectors are realized as a three-punctured-sphere compactification of a 6d theory and a D-type Argyres-Douglas theory, respectively, and this structure accounts for dualities and the flavor/symmetry properties across SU, USp, and SO theories. Upon soft N=1 perturbations, a finite number of confining vacua remains, tying together confinement dynamics with the underlying Seiberg-Witten geometry and confirming a unified infrared picture for these maximally singular points. The results also recover known special cases like Chebyshev points and connect to 6d constructions, offering a robust framework for exploring broader families of theories and dualities.

Abstract

We revisit the study of singular points in N=2 SQCD with classical gauge groups. Using a technique proposed recently by Gaiotto, Seiberg and Tachikawa we find that the low-energy physics at the maximally singular point involves two superconformal sectors coupled to an infrared free SU(2) gauge group. When one softly breaks extended supersymmetry to N=1 adding a mass term for the chiral multiplet in the adjoint representation, a finite number of vacua remain and the theory becomes confining. Our analysis allows to identify the low-energy physics at these distinguished points in the moduli space. In some cases, which we will describe in detail, two sectors coupled to an infrared free SU(2) gauge group emerge as before. For USp and SO gauge groups one of these sectors is always free, contrary to the SU case.

Paper Structure

This paper contains 7 sections, 55 equations, 2 figures.

Table of Contents

  1. Introduction
  2. $SU(N)$ SQCD with $2n$ flavors and r-vacua
  3. $USp(2N)$ SQCD with $2n$ flavors
  4. $SO(N)$ SQCD
  5. $SO(2N)$ SQCD with $2n$ flavors
  6. $SO(2N+1)$ SQCD with $2n+1$ flavors
  7. Conclusions

Figures (2)

  • Figure 1: The three punctured sphere that represents the theory entering in the S dual description of $USp(2N)$ with $2N+2$ flavors (in this case $N=3$).
  • Figure 2: The three punctured sphere associated to the SCFT entering in the S dual description of $SO(2N)$ with $2N-2$ flavors (in this case $N=4$). The black dot indicates the D-partition and we have drawn the corresponding Young tableau. The two maximal C-partitions are indicated with $\star$. To visualize the presence of the twist we draw a dashed line.