Laplace operators on Sasaki-Einstein manifolds

TL;DR

This paper analyzes the spectrum of the Laplace operator on Sasaki-Einstein manifolds, deriving bounds that relate to supergravity and superconformal field theories, using generalized Kahler identities.

Contribution

It introduces a decomposition of the de Rham Laplacian on Sasaki-Einstein manifolds and establishes spectrum bounds linked to supergravity and field theory unitarity.

Findings

Derived lower bounds on the Laplacian spectrum.

Connected spectrum bounds to supergravity unitarity conditions.

Generalized Kahler identities for Sasaki-Einstein manifolds.

Abstract

We decompose the de Rham Laplacian on Sasaki-Einstein manifolds as a sum over mostly positive definite terms. An immediate consequence are lower bounds on its spectrum. These bounds constitute a supergravity equivalent of the unitarity bounds in dual superconformal field theories. The proof uses a generalization of Kahler identities to the Sasaki-Einstein case.