Large Landscape of 4d Superconformal Field Theories from Small Gauge Theories

TL;DR

This paper systematically classifies a vast landscape of 4d $ ext{N}=1$ superconformal fixed points from small gauge theories, revealing new phenomena, dualities, and a rich statistical structure of their properties.

Contribution

It provides the first comprehensive classification of over 7,300 fixed points from small gauge theories, uncovering new SCFTs, dualities, and non-perturbative phenomena.

Findings

Identified 7,346 inequivalent fixed points with consistent properties.

Discovered a new SCFT with smaller central charges than known theories.

Revealed statistical patterns in central charges and operator dimensions.

Abstract

We systematically explore the space of renormalization group flows of four-dimensional $\mathcal{N}=1$ superconformal field theories (SCFTs) triggered by relevant deformations, as well as by coupling to free chiral multiplets with relevant operators. In this way, we classify all possible fixed point SCFTs that can be obtained from certain rank 1 and 2 supersymmetric gauge theories with small amount of matter multiplets, identifying 7,346 inequivalent fixed points which pass a series of non-trivial consistency checks. This set of fixed points exhibits interesting statistical behaviors, including a narrow distribution of central charges $(a, c)$, a correlation between the number of relevant operators and the ratio $a/c$, and trends in the lightest operator dimension versus $a/c$. The ratio $a/c$ of this set is distributed between $0.7228$ and $1.2100$, where the upper bound is larger than that of previously known interacting SCFTs. Moreover, we find a plethora of highly non-perturbative phenomena, such as (super)symmetry enhancements, operator decoupling, non-commuting renormalization group flows, and dualities. We especially identify amongst these fixed points a new SCFT that has smaller central charges $(a, c) = (\frac{633}{2000},\frac{683}{2000})$ than that of the deformed minimal Argyres-Douglas theory, as well as novel Lagrangian duals for certain $\mathcal{N}=1$ deformed Argyres-Douglas theories. We provide a website https://qft.kaist.ac.kr/landscape to navigate through our set of fixed points.