Sine-Gordon =/= Massive Thirring, and Related Heresies

TL;DR

This paper clarifies the differences between Sine-Gordon and massive Thirring models as perturbed conformal field theories, revealing their distinct UV limits, field content, and implications for their S-matrices and related quantum field theories.

Contribution

It demonstrates that Sine-Gordon and massive Thirring models are fundamentally different theories with unique field contents and UV behaviors, challenging previous assumptions of their equivalence.

Findings

Sine-Gordon at the free-Dirac point is a two-boson theory with diagonal S-matrix

The sign of the S-matrix in the soliton sector should be reversed for arbitrary couplings

Existence of new quantum field theory classes with partition functions invariant under subgroups of the modular group

Abstract

By viewing the Sine-Gordon and massive Thirring models as perturbed conformal field theories one sees that they are different (the difference being observable, for instance, in finite-volume energy levels). The UV limit of the former (SGM) is a gaussian model, that of the latter (MTM) a so-called {\it fermionic} gaussian model, the compactification radius of the boson underlying both theories depending on the SG/MT coupling. (These two families of conformal field theories are related by a ``twist''.) Corresponding SG and MT models contain a subset of fields with identical correlation functions, but each model also has fields the other one does not, e.g. the fermion fields of MTM are not contained in SGM, and the {\it bosonic} soliton fields of SGM are not in MTM. Our results imply, in particular, that the SGM at the so-called ``free-Dirac point'' $\beta^2 = 4\pi$ is actually a theory of two interacting bosons with diagonal S-matrix $S=-1$, and that for arbitrary couplings the overall sign of the accepted SG S-matrix in the soliton sector should be reversed. More generally, we draw attention to the existence of new classes of quantum field theories, analogs of the (perturbed) fermionic gaussian models, whose partition functions are invariant only under a subgroup of the modular group. One such class comprises ``fermionic versions'' of the Virasoro minimal models.