Chiral Vertex Operators in Off-Conformal Theory: The Sine-Gordon Example

TL;DR

This paper investigates chiral vertex operators in the off-conformal sine-Gordon model, revealing unexpected properties such as scale-invariant behavior and unique Lorentz spins, differing from conformal theory predictions.

Contribution

It demonstrates that certain chiral vertex operators retain scale invariance and exhibit unique Lorentz spins in the non-conformal sine-Gordon model, challenging conformal field theory expectations.

Findings

Mandelstam operator remains massless in sine-Gordon theory.

Some vertex operators maintain scale invariance despite non-conformal interactions.

Vertex operators exhibit diverse Lorentz spin properties in the off-conformal setting.

Abstract

We study chiral vertex operators in the sine-Gordon [SG] theory, viewed as an off-conformal system. We find that these operators, which would have been primary fields in the conformal limit, have interesting and, in some ways, unexpected properties in the SG model. Some of them continue to have scale- invariant dynamics even in the presence of the non-conformal cosine interaction. For instance, it is shown that the Mandelstam operator for the bosonic representation of the Fermi field does {\it not} develop a mass term in the SG theory, contrary to what the real Fermi field in the massive Thirring model is expected to do. It is also shown that in the presence of the non-conformal interactions, some vertex operators have unique Lorentz spins, while others do not.