The central charge of supersymmetric AdS_5 solutions of type IIB supergravity

TL;DR

This work demonstrates that generic supersymmetric AdS5 solutions of type IIB supergravity admit a canonical contact structure on the internal manifold Y, dictated by the Reeb vector that encodes the R-symmetry of the dual N=1 SCFT. Central charges and dimensions of BPS wrapped D3-brane operators are expressed purely in terms of contact data, via the formulas a_{N=4}/a = 1/(2π)^3 ∫_Y σ ∧ dσ ∧ dσ and Δ(O_{Σ3}) = [2π N ∫_{Σ3} σ ∧ dσ] / [∫_Y σ ∧ dσ ∧ dσ], with a natural framing as Duistermaat–Heckman integrals and localization, respectively. In the quasi-regular (U(1)) R-symmetry case these quantities are rational, matching field theory expectations, and the approach extends familiar Sasaki–Einstein results to generic AdS5 backgrounds. The paper also discusses implications for a-maximization and potential generalizations to other AdS5 constructions, including D=11 analogs and the F5 = 0 limit.

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.