CP-violating CFT and trace anomaly

TL;DR

This paper explores the theoretical possibility of including the Hirzebruch-Pontryagin density in the trace anomaly of four-dimensional CP-violating conformal field theories, using holographic methods.

Contribution

It demonstrates, through holographic renormalization, that the Hirzebruch-Pontryagin term can appear in the trace anomaly, indicating CP violation in conformal field theories.

Findings

Hirzebruch-Pontryagin density can be part of the trace anomaly in CP-violating theories

The term vanishes at free conformal fixed points

Holographic renormalization confirms the possibility of such anomaly contributions

Abstract

It is logically possible that the trace anomaly in four dimension includes the Hirzebruch-Pontryagin density in CP violating theories. Although the term vanishes at free conformal fixed points, we realize such a possibility in the holographic renormalization group and show that it is indeed possible. The Hirzebruch-Pontryagin term in the trace anomaly may serve as a barometer to understand how much CP is violated in conformal field theories.