Parity-odd surface anomalies and correlation functions on conical defects

TL;DR

This paper investigates parity-odd surface anomalies in conformal field theories, focusing on conical defects in 3D and 4D spacetimes, revealing how bulk anomalies induce specific surface trace anomalies and contact terms in correlators.

Contribution

It constructs the general form of P-type surface trace anomalies on singular surfaces and links them to bulk anomalies, especially for conical defects in 3D and 4D.

Findings

Bulk P-type Pontryagin anomaly induces surface trace anomaly.

Surface contact terms are lower rank than bulk terms.

Surface anomalies are expressed via the outer curvature tensor.

Abstract

We analyse the parity-odd ("type P") surface anomalies of the energy-momentum tensor correlators in conformal field theories, with an emphasis on d=4 and d=3 dimensional spacetimes. Using cohomology analysis we construct the expression for the most general P-type surface trace anomaly on a singular 2-dimensional surface in 4-dimensional bulk spacetimes. As an important example, we specialise to the case when the singular surface is a conical defect and show that the bulk P-type Pontryagin trace anomaly induces such a surface trace anomaly. We show that this conical type P surface trace anomaly is given purely by the outer curvature tensor. In addition, we analyse parity-odd surface contact terms in energy-momentum tensor correlators in the flat spacetime induced by the conical defect by studying two special cases in which the contact terms are induced by, (1) type P trace anomaly in d=4 and, (2) gravitational Chern-Simons Lagrangian term in d=3 spacetime dimensions. In both cases we show that the surface contact terms appear in correlators of the lower rank than the corresponding bulk surface terms.