Triangle Anomalies from Einstein Manifolds

TL;DR

This paper derives a geometric formula for Chern-Simons couplings in type IIB supergravity on Einstein manifolds, linking gravity and gauge theory anomalies and revealing connections with giant graviton condensations.

Contribution

It provides a simple geometric expression for Chern-Simons couplings in supergravity compactifications on Einstein manifolds, matching gauge theory results.

Findings

Gravity results agree with quiver gauge theory for specific Einstein manifolds.

The analysis uncovers a link between anomalies and giant graviton condensations.

The formula applies to circle bundles over del Pezzo surfaces and toric Sasaki-Einstein manifolds.

Abstract

The triangle anomalies in conformal field theory, which can be used to determine the central charge a, correspond to the Chern-Simons couplings of gauge fields in AdS under the gauge/gravity correspondence. We present a simple geometrical formula for the Chern-Simons couplings in the case of type IIB supergravity compactified on a five-dimensional Einstein manifold X. When X is a circle bundle over del Pezzo surfaces or a toric Sasaki-Einstein manifold, we show that the gravity result is in perfect agreement with the corresponding quiver gauge theory. Our analysis reveals an interesting connection with the condensation of giant gravitons or dibaryon operators which effectively induces a rolling among Sasaki-Einstein vacua.