Holographic spectral functions for Sasaki-Einstein 5-manifolds

TL;DR

This paper develops a spectral framework for analyzing holographic properties of Sasaki-Einstein 5-manifolds, enabling the computation of geometric invariants and anomalies for both toric and non-toric cases.

Contribution

It introduces a new spectral approach to compute holographic invariants and anomalies for general Sasaki-Einstein manifolds, extending beyond toric geometries.

Findings

Computed curvature-squared integrals and anomalies using supersymmetric zeta functions.

Developed a combinatorial method for toric Sasaki-Einstein manifolds.

Extended spectral analysis framework to non-toric geometries.

Abstract

We investigate holographic spectral functions for general Sasaki-Einstein 5-manifolds dual to four-dimensional superconformal field theories, including supersymmetric indices, supersymmetric zeta functions, and supersymmetric determinants. The analytic structure of the supersymmetric zeta function, particularly its residue and special value, allows for the computation of the curvature-squared integral of the Sasaki-Einstein manifold and the subleading holographic anomaly. The reach of this spectral framework is not restricted to toric geometries and accommodates non-toric Sasaki-Einstein manifolds. For toric Sasaki-Einstein manifolds, we develop a combinatorial method to compute the holographic spectral functions and the holographic geometric invariants directly from the toric data.