Renormalized new solutions for the massless Thirring model

TL;DR

This paper non-perturbatively analyzes the massless Thirring model using path integrals, revealing new solutions due to regularization ambiguities and identifying two distinct quantum phases with different symmetries.

Contribution

It introduces new solution types for the massless Thirring model arising from regularization ambiguities and distinguishes two quantum phases based on Ward identities.

Findings

Discovery of a new symmetric phase with local gauge symmetry.

Identification of solutions related to known models for specific ambiguity parameters.

Detailed analysis of UV divergences and successful non-perturbative renormalization.

Abstract

We present a non--perturbative study of the (1+1)--dimensional massless Thirring model by using path integral methods. The regularization ambiguities -coming from the computation of the fermionic determinant- allow to find new solution types for the model. At quantum level the Ward identity for the 1PI 2-point function for the fermionic current separates such solutions in two phases or sectors, the first one has a local gauge symmetry that is implemented at quantum level and the other one without this symmetry. The symmetric phase is a new solution which is unrelated to the previous studies of the model and, in the non--symmetric phase there are solutions that for some values of the ambiguity parameter are related to well-known solutions of the model. We construct the Schwinger--Dyson equations and the Ward identities. We make a detailed analysis of their UV divergence structure and, after, we perform a non--perturbative regularization and renormalization of the model.