Logarithmic Correlators in Non-relativistic Conformal Field Theory

TL;DR

This paper investigates the emergence of logarithmic terms in correlators within non-relativistic conformal field theories, specifically focusing on the Schrodinger-Virasoro and affine Galilean Conformal algebras, revealing unique structural properties.

Contribution

It demonstrates how logarithmic terms can appear in correlators of fields in these algebras and clarifies the conditions under which Jordanian forms occur.

Findings

Logarithmic dependence appears along the time direction only.

In GCA, only scaling operators can have Jordanian forms.

Logarithmic terms are associated with specific algebraic structures.

Abstract

We show how logarithmic terms may arise in the correlators of fields which belong to the representation of the Schrodinger-Virasoro algebra (SV) or the affine Galilean Conformal Algebra (GCA). We show that in GCA, only scaling operator can have a Jordanian form and rapidity can not. We observe that in both algebras logarithmic dependence appears along the time direction alone.