Yukawa CFTs and Emergent Supersymmetry

TL;DR

This paper investigates Yukawa conformal field theories in dimensions between 2 and 4, providing new evidence for emergent supersymmetry and analyzing their properties using epsilon expansions, Pade approximants, and conformal bootstrap comparisons.

Contribution

It offers the first epsilon expansion calculations for Yukawa CFTs with supersymmetry and demonstrates their consistency with bootstrap results and known models.

Findings

Evidence that N=1 Yukawa theory flows to a supersymmetric CFT in 3D.

Support for emergent supersymmetry in N=2 Nambu-Jona-Lasinio-Yukawa model.

Continuations suggest flow to tri-critical Ising model in 2D.

Abstract

We study conformal field theories with Yukawa interactions in dimensions between 2 and 4; they provide UV completions of the Nambu-Jona-Lasinio and Gross-Neveu models which have four-fermion interactions. We compute the sphere free energy and certain operator scaling dimensions using dimensional continuation. In the Gross-Neveu CFT with $N$ fermion degrees of freedom we obtain the first few terms in the $4-\epsilon$ expansion using the Gross-Neveu-Yukawa model, and the first few terms in the $2+\epsilon$ expansion using the four-fermion interaction. We then apply Pade approximants to produce estimates in $d=3$. For $N=1$, which corresponds to one 2-component Majorana fermion, it has been suggested that the Yukawa theory flows to a ${\cal N}=1$ supersymmetric CFT. We provide new evidence that the $4-\epsilon$ expansion of the $N=1$ Gross-Neveu-Yukawa model respects the supersymmetry. Our extrapolations to $d=3$ appear to be in good agreement with the available results obtained using the numerical conformal bootstrap. Continuation of this CFT to $d=2$ provides evidence that the Yukawa theory flows to the tri-critical Ising model. We apply a similar approach to calculate the sphere free energy and operator scaling dimensions in the Nambu-Jona-Lasinio-Yukawa model, which has an additional $U(1)$ global symmetry. For $N=2$, which corresponds to one 2-component Dirac fermion, this theory has an emergent supersymmetry with 4 supercharges, and we provide new evidence for this.