# 2d Galilean Field Theories with Anisotropic Scaling

## TL;DR

This paper explores two-dimensional Galilean field theories with anisotropic scaling, revealing enhanced symmetries, formulating a covariant Newton-Cartan geometric framework, and deriving key properties like correlation functions and Cardy-like formulas.

## Contribution

It introduces a covariant Newton-Cartan geometric approach to anisotropic Galilean theories and establishes their symmetry structure and thermodynamic properties.

## Key findings

- Enhanced local symmetries via infinite dimensional algebra
- Covariant formulation using Newton-Cartan geometry
- Derivation of Cardy-like formulas for partition functions

## Abstract

In this work, we study two-dimensional Galilean field theories with global translations and anisotropic scaling symmetries. We show that such theories have enhanced local symmetries, generated by the infinite dimensional spin-l Galilean algebra with possible central extensions, under the assumption that the dilation operator is diagonalizable and has a discrete and non-negative spectrum. We study the Newton-Cartan geometry with anisotropic scaling, on which the field theories could be defined in a covariant way. With the well-defined Newton-Cartan geometry we establish the state-operator correspondence in anisotropic GCFT, determine the two-point functions of primary operators, and discuss the modular properties of the torus partition function which allows us to derive Cardy-like formulae.