Type IIB Supergravity Action and Holography

TL;DR

This paper refines the Type IIB supergravity action by introducing a generalized topological correction, enabling accurate holographic calculations directly in ten dimensions for a broader class of backgrounds, including AdS geometries.

Contribution

It extends the Pasti-Sorokin-Tonin formulation to include a generalized topological term applicable to diverse Type IIB backgrounds, improving holographic correspondence calculations.

Findings

Agreement with lower-dimensional supergravity on-shell actions.

Successful application to non-trivial backgrounds like Lunin-Maldacena.

Enhanced consistency of holographic computations in ten dimensions.

Abstract

In the prototypical AdS$_5$/CFT$_4$ correspondence, the free energy of $\mathcal{N}=4$ SU$(N)$ super Yang-Mills theory is commonly reproduced from the Euclidean on-shell action of five-dimensional gauged supergravity -- a consistent truncation of Type IIB supergravity -- rather than computed directly in ten dimensions. A longstanding obstacle to the latter is that the conventional Type IIB pseudo-action evaluated on the $AdS_5\times S^5$ background vanishes identically, apparently precluding a first-principles holographic comparison. A recent proposal by Kurlyand and Tseytlin, based on the Pasti-Sorokin-Tonin formulation, resolves this issue for a special class of backgrounds including the $AdS_5\times S^5$ vacuum by introducing a topological term required for consistency, yielding a non-vanishing on-shell value in agreement with holography. In this work we extend this refinement to a broader class of Type IIB backgrounds by introducing a generalized topological correction under milder conditions, encompassing AdS geometries of generic dimension and non-vanishing 2-form potentials. We test the proposal on non-trivial solutions such as the Lunin-Maldacena background and the $AdS_4$ $S$-fold solution, and find agreement with the corresponding lower-dimensional gauged supergravity on-shell actions and thereby with the expected holographic observables. Our results place direct holographic comparisons within the ten-dimensional Type IIB framework on firmer ground.