Generating Charge from Diffeomorphisms

TL;DR

This paper explores how coordinate transformations generate charges in AdS_q imes S^p spacetimes, linking bulk properties to boundary CFT spectral flow and revealing the origins of anomalies and Chern-Simons terms.

Contribution

It provides explicit formulas for angular momentum charges and clarifies the role of p-form fields in generating these charges in higher-dimensional AdS spaces.

Findings

Charges can be generated by coordinate transformations in AdS_3.

The analysis links bulk properties to boundary spectral flow.

Reveals the higher-dimensional origin of Chern-Simons terms and anomalies.

Abstract

We unravel some subtleties involving the definition of sphere angular momentum charges in AdS_q \times S^p spacetimes, or equivalently, R-symmetry charges in the dual boundary CFT. In the AdS_3 context, it is known that charges can be generated by coordinate transformations, even though the underlying theory is diffeomorphism invariant. This is the bulk version of spectral flow in the boundary CFT. We trace this behavior back to special properties of the p-form field strength supporting the solution, and derive the explicit formulas for angular momentum charges. This analysis also reveals the higher dimensional origin of three dimensional Chern-Simons terms and of chiral anomalies in the boundary theory.