A landscape of 4d N=1 SCFTs with a=c

TL;DR

This work builds a comprehensive landscape of 4d N=1 SCFTs with identical central charges by starting from gauged Argyres-Douglas matter and exploring all supersymmetry-preserving superpotential deformations. Focusing on the seed theory of three D2(SU(3)) blocks gauged with an adjoint, it catalogues an extensive network of a = c fixed points, uncovering diverse dualities and supersymmetry-enhancement phenomena, including flows to N=4 SYM and to free vector multiplets. The methodology blends a-maximization, anomaly matching, and index checks to identify consistent IR R-symmetries and central charges, while tracking operator spectra and unitarity constraints along RG flows. The findings reveal a rich interconnected web of fixed points, many linked by dualities, suggesting deep ties between a=c theories and higher-supersymmetry structures, with potential holographic interpretations via domain-wall solutions. This work lays groundwork for broader LANDSCAPE studies (LANDSCAPE II and III) and points to intriguing universal patterns in a=c landscapes across gauged Argyres-Douglas theories.

Abstract

We study a landscape of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) with identical central charges. These theories are obtained by renormalization group flows triggered by supersymmetry-preserving superpotential deformations of the $\mathcal{N}=1$ gauging of the flavor symmetry of a collection of $\mathcal{N}=2$ $\mathcal{D}_p(G)$ Argyres--Douglas SCFTs. In this work, we focus on the fixed points in the landscape of the $SU(3)$ gauging of three copies of the $\mathcal{D}_2(SU(3)) = H_2$ theory together with an adjoint-valued chiral multiplet. We catalogue the network of $a = c$ fixed points, and, along the way, we find a variety of dualities and instances of supersymmetry enhancement.

Figures (3)

• Figure 1.1: An asymptotically-free $\mathcal{N}=1$ gauge theory via the diagonal gauging of the $SU(3)$ flavor symmetry of three copies of the $\mathcal{D}_2(SU(3))$ Argyres--Douglas theory, via $\mathcal{N}=1$ vector multiplets, with an adjoint-valued chiral multiplet, which is depicted as a dashed arrow line.
• Figure 1.2: The network of $a=c$ SCFT preserving superpotential deformations of the gauged Argyres--Douglas theory depicted in Figure \ref{['fig:deformations']}. In each box, we describe the fixed point (possibly in a dual frame) as well as giving the value of the coefficient of the central charges. We write $(2, \cdots, 2)$ to denote the number of gauged $\mathcal{D}_2(G)$s. See Section \ref{['sec:222landscape']} for the derivation of this landscape.
• Figure 2.1: We schematically depict our construction of 4d $\mathcal{N}=1$ gauge theories via a collection of $n$ Argyres--Douglas theories $\mathcal{D}_{p_\alpha}$ that are diagonally gauged via an $\mathcal{N}=1$ vector multiplet. We can also include up to three adjoint-valued chiral multiplets.