Holographic origin of $a$-maximization and higher-derivative AdS$_5$/CFT$_4$
Kiril Hristov, Saurish Khandelwal, Yi Pang, Gabriele Tartaglino-Mazzucchelli
TL;DR
The paper develops a partially off-shell framework for higher-derivative corrections in 5d ${ m N}=1$ gauged supergravity on AdS$_5$, establishing a direct holographic link between Chern-Simons couplings and the 4d anomaly polynomial. By organizing invariants via off-shell multiplets and BF-type actions, it shows that the holographic trial $a$-anomaly equals the off-shell AdS$_5$ action, with the on-shell extremization implementing $a$-maximization. The authors classify two- and four-derivative invariants, including novel off-diagonal terms, and demonstrate that higher-derivative invariants do not introduce new CS terms on BPS AdS$_5$ backgrounds, reducing to linear combinations of the known actions. This provides a robust, anomaly-driven route to exact results for supersymmetric observables in AdS$_5$/CFT$_4$, beyond the strict large-$N$ or two-derivative limits. The work opens avenues for incorporating gauged hypermultiplets and fully leveraging the anomaly structure to constrain holographic data.
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.