One-Loop Quantum Effects in Carroll Scalars

TL;DR

This paper investigates whether the infinite supertranslation symmetries of classical Carrollian scalar field theories persist after quantum corrections, revealing a new fixed point in the renormalization group flow.

Contribution

It demonstrates that classical Carrollian symmetries survive quantum effects for polynomial interactions and introduces a specialized renormalization group analysis respecting Carroll invariance.

Findings

Classical supertranslation symmetries are preserved at quantum level for polynomial interactions.

A new non-Gaussian fixed point is identified in the Carroll-invariant renormalization group flow.

Carroll-breaking deformations influence the fixed point structure and flow dynamics.

Abstract

Carrollian field theories at the classical level possess an infinite number of space-time symmetries, namely the supertranslations. In this article, we inquire whether these symmetries for interacting Carrollian scalar field theory survive in the presence of quantum effects. For interactions polynomial in the field, the answer is in the affirmative. We also study a renormalization group flow particularly tailored to respect the manifest Carroll invariance and analyze the consequences of introducing Carroll-breaking deformations. The renormalization group flow, with perturbative loop-level effects taken into account, indicates a new fixed point apart from the Gaussian ones.