On Instantons in Gross-Neveu and Gross-Neveu-Yukawa models

TL;DR

This paper investigates fermionic instantons in Gross-Neveu and Gross-Neveu-Yukawa models, deriving solutions, analyzing actions at fixed points, and relating them to sphere mappings and large N computations.

Contribution

It provides explicit solutions for fermionic instantons in both models and connects these to fixed point actions and large N results, offering new insights into their non-perturbative structure.

Findings

Derived explicit instanton solutions for both models

Mapped solutions onto the sphere and related to Hubbard-Stratonovich approach

Compared fixed point actions with large N computations

Abstract

We study fermionic instantons of the Gross-Neveu and the Gross-Neveu-Yukawa models. We derive solutions for both models and examine the corresponding actions at the fixed points. We further map the solutions on to the sphere and discuss the relation to the Hubbard-Stratonovich approach. Close to the fixed points we compare and identify the results with those obtained in the large $N$ computation.