Conformal Models of Thirring Type and the Affine Virasoro Construction

TL;DR

This paper studies 1+1 dimensional fermionic models with four-fermion interactions, showing that at specific couplings they become conformally invariant, restoring Lorentz symmetry in a non-perturbative quantum context.

Contribution

It demonstrates the emergence of conformal invariance and Lorentz symmetry restoration at special coupling values in a class of fermionic models, combining perturbative and non-perturbative analysis.

Findings

Models are ultraviolet finite at each perturbation order

Lorentz symmetry is restored at specific coupling constants

Models exhibit conformal invariance at these special points

Abstract

We investigate a class of models in 1+1 dimensions with four fermion interaction term. At each order of the perturbation expansion, the models are ultraviolet finite and Lorentz non-invariant. We show that for certain privileged values of the coupling constants, Lorentz symmetry is restored, and indeed the model turns out to be conformally invariant. This phenomenon is both quantum mechanical and non-perturbative.