Bounding irrelevant operators in the 3d Gross-Neveu-Yukawa CFTs

TL;DR

This paper uses numerical bootstrap methods to establish bounds on scalar operator dimensions in 3d Gross-Neveu-Yukawa models, constraining the number of relevant operators and informing RG flow analysis.

Contribution

It provides the first rigorous bounds on the next-to-lowest scalar operator dimensions in these models for N=2, 4, 8, revealing only two relevant singlet scalars.

Findings

All bounds on scalar dimensions are greater than 3.

Only two relevant singlet scalars exist in these models.

Constraints are placed on the RG flow structure.

Abstract

We perform a numerical bootstrap study of scalar operators in the critical 3d Gross-Neveu-Yukawa models, a family of conformal field theories containing N Majorana fermions in the fundamental representation of an O(N) global symmetry. We compute rigorous bounds on the scaling dimensions of the next-to-lowest parity-even and parity-odd singlet scalars at N = 2, 4, and 8. All of these dimensions have lower bounds greater than 3, implying that there are only two relevant singlet scalars and placing constraints on the RG flow structure of these theories.