Anomalies and Parity-Violating Interactions: From Conformal to Thermal Field Theory

TL;DR

This paper explores chiral and conformal anomalies within conformal and thermal field theories, focusing on their mathematical structure, physical implications, and how they are affected by conditions like finite temperature, density, and fermion mass.

Contribution

It provides a detailed analysis of parity-odd interactions and anomalies in conformal field theory, highlighting their behavior under thermal and density effects, and clarifies the role of conformal Ward identities.

Findings

Conformal Ward identities fully characterize parity-odd interactions.

Finite temperature and density can break conformal invariance.

Parity-odd anomalous interactions exhibit specific behaviors under thermal conditions.

Abstract

Chiral and conformal anomalies are fundamental phenomena that span multiple disciplines, including high-energy physics, condensed matter theory and cosmology. These anomalies play a crucial role in understanding fundamental interactions and manifest themselves through divergences and traces of correlation functions. In this thesis, we investigate these phenomena within the framework of conformal field theory, elucidating their intricate structure and physical implications. Our primary focus is on the role of conformal Ward identities in fully characterizing parity-odd interactions associated with chiral and conformal anomalies in momentum space. Furthermore, we explore mechanisms that lead to the breaking of conformal invariance, such as finite-temperature and finite-density effects or the presence of a fermion mass, and examine how parity-odd anomalous interactions behave under these conditions. By analyzing these phenomena through the lens of conformal and thermal field theories, we obtain deeper insights into their mathematical structure and their significance across a wide range of physical contexts.