Boundary-Value Problem in Type IIB Supergravity and Holography
Abstract
In precision holography, the Euclidean on-shell action of type IIB supergravity often fails to reproduce the leading large-N free energy of the dual field theory: the type IIB pseudo action, for instance, vanishes identically on the EAdS5× S5 background. We address this issue by revisiting the boundary-value problem of the Euclidean type IIB pseudo action from first principles. Classifying the admissible boundary conditions through the variational principle, we construct a generalized pseudo action whose boundary terms implement the choice of ensemble --- fixed potentials versus fixed quantized Page charges --- in which the holographic comparison is performed. For the fixed five-form-charge ensemble, the resulting boundary term reproduces the recently proposed topological correction to the Pasti--Sorokin--Tonin formulation of type IIB supergravity for holographic backgrounds of interest. We then test the generalized pseudo action on two complementary backgrounds: the EAdS3× S3× M4 near-horizon geometry of the D1-D5 system and the warped EAdS6× S2×Σ solutions dual to five-dimensional SCFTs. In both cases the ten-dimensional on-shell action agrees exactly with that of the corresponding lower-dimensional supergravity, and thereby with the leading large-N free energy of the dual SCFT. Our results establish the choice of boundary conditions --- and hence of ensemble --- as an essential ingredient of precision holography directly in type IIB supergravity, extending recent analyses in eleven-dimensional supergravity.
Related
- Derivation of the General Solution of the Black-Scholes Boundary-Value Problem
- Frustration-Free Models for Topological Holography: Fusion Spin Chains as Boundary Algebras
- The Komar charges of type II supergravity and supersymmetric localization
- Null String Holography, Null Strings Probe Projective Boundary of Their Target Spaces
- de Sitter and S-folds in type IIB from 𝒩 = 4 D = 4 gauged supergravity
BibTeX
@misc{adhikari2026boundaryvalue,
title = {{Boundary-Value Problem in Type IIB Supergravity and Holography}},
author = {Soumya Adhikari and Junho Hong and Chanyoung Joung and Geum Lee and Sourav Roychowdhury},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03126},
eprint = {2609.03126},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03126},
}
RIS
TY - UNPB
TI - Boundary-Value Problem in Type IIB Supergravity and Holography
AU - Soumya Adhikari
AU - Junho Hong
AU - Chanyoung Joung
AU - Geum Lee
AU - Sourav Roychowdhury
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.03126
UR - https://arxiv.org/abs/2609.03126
AB - In precision holography, the Euclidean on-shell action of type IIB supergravity often fails to reproduce the leading large-N free energy of the dual field theory: the type IIB pseudo action, for instance, vanishes identically on the EAdS_5× S^5 background. We address this issue by revisiting the boundary-value problem of the Euclidean type IIB pseudo action from first principles. Classifying the admissible boundary conditions through the variational principle, we construct a generalized pseudo action whose boundary terms implement the choice of ensemble --- fixed potentials versus fixed quantized Page charges --- in which the holographic comparison is performed. For the fixed five-form-charge ensemble, the resulting boundary term reproduces the recently proposed topological correction to the Pasti--Sorokin--Tonin formulation of type IIB supergravity for holographic backgrounds of interest. We then test the generalized pseudo action on two complementary backgrounds: the EAdS_3× S^3× M_4 near-horizon geometry of the D1-D5 system and the warped EAdS_6× S^2×Σ solutions dual to five-dimensional SCFTs. In both cases the ten-dimensional on-shell action agrees exactly with that of the corresponding lower-dimensional supergravity, and thereby with the leading large-N free energy of the dual SCFT. Our results establish the choice of boundary conditions --- and hence of ensemble --- as an essential ingredient of precision holography directly in type IIB supergravity, extending recent analyses in eleven-dimensional supergravity.
ER -