Infinitely many 4d N=1 SCFTs with a=c

TL;DR

The paper demonstrates that there exist infinitely many 4d $\mathcal{N}=1$ SCFTs with equal central charges $a=c$ by diagonally gauging the flavor symmetry $G$ of a collection of $\mathcal{D}_p(G)$ Argyres–Douglas theories, with or without adjoint chiral multiplets. The core method uses $a$-maximization and NSVZ-type anomaly constraints to identify when IR fixed points satisfy $a=c$, revealing a robust set of admissible $(p_i)$ configurations (under $\gcd(p_i,h_G^\vee)=1$) that yield interacting SCFTs. They show explicit results for up to five glued $\mathcal{D}_p(G)$ theories and a conformal gauging of six $\mathcal{D}_2(G)$ theories, all producing $a=c$ in the IR, and they explore extensions with adjoint chiral matter, mass deformations, and Lagrangian realizations. Beyond these, the work discusses obstructions and partial results when including conformal matter, and outlines potential holographic and geometric avenues to realize and classify these $a=c$ theories, indicating a vast landscape of minimally supersymmetric CFTs with equal central charges. The findings illuminate how exactly marginal operators and anomaly constraints shape the IR structure and central-charge relations in intricate $\mathcal{N}=1$ constructions.

Abstract

We study a rich set of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with both central charges identical: $a = c$. We construct them via the diagonal $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres--Douglas theories of type $\mathcal{D}_p(G)$, with or without additional adjoint chiral multiplets. In this way, we construct infinitely-many theories that flow to interacting SCFTs with $a = c$ in the infrared. Finally, we briefly highlight the features of the SCFTs without $a = c$ that arise from generalizing this construction.

Figures (11)

• Figure 1.1: RG flows triggered by the mass deformation of the $\mathcal{N}=2$ theory vs gauging an $\mathcal{N}=1$ vector multiplet. The red cross is to emphasize that there is no direct renormalization group flow between the $\mathcal{N}=2$ gauging and the $\mathcal{N}=1$ gauging.
• Figure 2.1: Contour plots of $-\epsilon_1$ and $-\epsilon_3\cdot p_3$. We see that $\epsilon_1$ lies in the range $\left(-\frac{1}{3},0\right)$, and thus $\epsilon_2$ does also. In (b) we show that $-\epsilon_3\cdot p_3$ is always positive, and since we are in a large $p_3$ limit then we can see that $\epsilon_3$ must also lie in the range $\left(-\frac{1}{3},0\right)$.
• Figure 2.2: Contours plot of $\epsilon_1$ and $\epsilon_3$ in the $(p_1,p_2)$ plane for $p_3=2,3,4$. They all satisfy the unitarity condition in equation \ref{['eq:unit_cond']}.
• Figure 2.3: Contour plot of $-\epsilon_1$ and $-\epsilon_3$ for $(p_1,p_2,p_3,p_4)=(2,2,p_3,p_4)$. Every R-symmetry mixing coefficient $\epsilon_i$ satisfies the unitarity condition in equation \ref{['eq:unit_cond']}.
• Figure 2.4: Plot of $\epsilon_{1,2,3,4}$ in gluing four $\mathcal{D}_{p_i}(G)$ theories with all $(p_1,p_2,p_3,p_4)$ listed in Table \ref{['tbl:asympfreep']}, except first case, $(2,2,p_3,p_4)$, which is numerically studied in Figure \ref{['fig:a_4g_large']}. All the coefficients are in the range prescribed in equation \ref{['eq:unit_cond']}.