Studies on Carrollian Quantum Field Theories

TL;DR

This work tackles gauge-dependence issues in Carrollian quantum fields, showing that the renormalized mass in scalar Carrollian electrodynamics becomes gauge-independent only when the theory is fully gauge-fixed, otherwise leaving spurious loop corrections. It provides a canonical quantization framework for complex Carrollian scalars and Carrollian fermions and presents a functional analysis of Carrollian electrodynamics, highlighting ultra-local correlators and the role of gauge fixing in revealing physical degrees of freedom. Through BRST symmetry and Nielsen identities, the authors demonstrate that physical masses are ξ-independent under complete gauge fixing, resolving prior contradictions and clarifying the structure of sCED. The results have implications for flat-space holography, suggesting Abelian Carrollian gauge theories may be unsuitable as boundary duals due to their trivial quantum dynamics, and pointing toward non-Abelian theories for nontrivial holographic realizations, with future work extending to conformal, magnetic-sector, and non-Abelian Carrollian QFTs.

Abstract

We examine the quantum field description of massive Carrollian field theories, emphasizing the critical role of gauge fixing within the Carrollian sector. We illustrate this importance using scalar Carrollian Electrodynamics (sCED) as a primary example. We also present the quantum field description for complex Carrollian scalar fields, Carrollian fermions, and Carrollian Electrodynamics. We highlight the challenges in scalar Carrollian electrodynamics (sCED), where the renormalized mass appears gauge-dependent, and clarify this discrepancy by carefully constructing completely gauge-fixed propagators. We discuss how certain abelian Carrollian field theories do not admit any loop corrections and are trivial in that sense.