Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories

TL;DR

This paper investigates how conformal symmetry constrains operator product expansions and 3-point functions in nonrelativistic conformal field theories, revealing unique features compared to relativistic cases and discussing conservation laws.

Contribution

It demonstrates that in nonrelativistic CFTs, 3-point functions of primaries with particle number are determined up to a coefficient, and explores the structure of primaries with zero particle number.

Findings

3-point functions with nonzero particle number are fixed up to a coefficient

OPE coefficients of descendants relate to primaries as in relativistic CFTs

Conservation laws influence the structure of zero particle number primaries

Abstract

We explore the consequences of conformal symmetry for the operator product expansions in nonrelativistic field theories. Similar to the relativistic case, the OPE coefficients of descendants are related to that of the primary. However, unlike relativistic CFTs the 3-point function of primaries is not completely specified by conformal symmetry. Here, we show that the 3-point function between operators with nonzero particle number, where (at least) one operator has the lowest dimension allowed by unitarity, is determined up to a numerical coefficient. We also look at the structure of the family tree of primaries with zero particle number and discuss the presence of conservation laws in this sector.