The fate of conformal symmetry in the non-linear Schr\"{o}dinger theory

TL;DR

This paper investigates how quantum corrections affect conformal symmetry in non-linear Schrödinger theories, showing that quantum effects break the classical symmetry through an anomalous contribution linked to the beta-function.

Contribution

It provides a detailed quantum analysis of conformal symmetry breaking in non-linear Schrödinger theories, especially for Phi^4-theory in two dimensions.

Findings

Quantum corrections break classical conformal symmetry.

Anomalous contributions are proportional to the beta-function.

Symmetry preservation depends on the specific dimension and interaction.

Abstract

The free Schroedinger theory in d space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in particular for the Phi^4-theory in d = 2. We compute the full quantum corrections to the 4-point function to show that the symmetry is broken by an anomalous contribution proportional to the exact beta-function