The central charge of supersymmetric AdS_5 solutions of type IIB supergravity

TL;DR

This paper demonstrates that supersymmetric AdS_5 solutions in type IIB supergravity have a canonical contact structure that determines key physical quantities, enabling calculations of the central charge and operator dimensions from partial solution data.

Contribution

It introduces a canonical contact structure for supersymmetric AdS_5 solutions, linking geometric data to physical quantities and proving their rationality under certain symmetries.

Findings

Central charge and operator dimensions are determined by the contact structure.

Both quantities are rational numbers for solutions with U(1) R-symmetry.

The approach involves Duistermaat-Heckman integrals and localization techniques.

Abstract

We show that generic supersymmetric AdS_5 solutions of type IIB supergravity admit a canonical contact structure. This structure determines the central charge of the dual field theory and the conformal dimension of operators dual to supersymmetric wrapped D3-branes. Hence both quantities can be calculated using incomplete information about the solutions, allowing us to prove that they are rational numbers for solutions with a U(1) R-symmetry, in agreement with field theory expectations. We also discuss related Duistermaat-Heckman integrals and localization formulae.