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arXiv · 2511.22546

Holographic origin of $a$-maximization and higher-derivative AdS$_5$/CFT$_4$

Kiril Hristov·Saurish Khandelwal·Yi Pang·Gabriele Tartaglino-Mazzucchelli
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Abstract

We develop a consistent partially off-shell framework for evaluating higher-derivative actions of five-dimensional $\cal{N}=1$ gauged supergravity with abelian vector multiplets on AdS$_5$. Using the superconformal formalism, we show that the resulting holographic expression reproduces the trial $a$-anomaly coefficient of the dual conformal field theory, identifying the supergravity equations of motion with $a$-maximization. We present an exact correspondence between Chern-Simons couplings and the anomaly polynomial of the boundary theory. We illustrate our proposal by applying it to all known two- and four-derivative actions, including the ``off-diagonal'' invariants never before considered in the gauged supergravity literature. Finally, we argue that all invariants beyond four-derivative yield no genuinely new contributions to asymptotically AdS$_5$ BPS backgrounds, but instead reduce to linear combinations of the established two- and four-derivative actions.

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Kiril Hristov, Saurish Khandelwal, Yi Pang, Gabriele Tartaglino-Mazzucchelli. 2025-11-27. Holographic origin of $a$-maximization and higher-derivative AdS$_5$/CFT$_4$. https://doi.org/10.1103/nrlq-ktd1

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