The Gross-Neveu-Yukawa Archipelago

TL;DR

This paper uses bootstrap techniques to rigorously bound the scaling dimensions of Gross-Neveu-Yukawa fixed points in 3d CFTs with O(N) symmetry, focusing on N=1, 2, 4, 8 relevant to condensed matter phase transitions.

Contribution

It provides the first rigorous bounds on GNY fixed points in 3d CFTs with O(N) symmetry, identifying isolated regions in the space of CFT data for specific N values.

Findings

Bounds tightly constrain GNY fixed points in 3d CFTs.

Results compare favorably with previous analytical and numerical studies.

Isolated islands in CFT data space indicate well-defined fixed points.

Abstract

We perform a bootstrap analysis of a mixed system of four-point functions of bosonic and fermionic operators in parity-preserving 3d CFTs with O(N) global symmetry. Our results provide rigorous bounds on the scaling dimensions of the O(N)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live in isolated islands in the space of CFT data. We focus on the cases N = 1, 2, 4, 8, which have applications to phase transitions in condensed matter systems, and compare our bounds to previous analytical and numerical results.