Higher-derivative supergravity, AdS4 holography, and black holes

Abstract

We use conformal supergravity techniques to study four-derivative corrections in four-dimensional gauged supergravity. We show that the four-derivative Lagrangian for the propagating degrees of freedom of the $$ \mathcal{N} $$ N = 2 gravity multiplet is determined by two real dimensionless constants. We demonstrate that all solutions of the two-derivative equations of motion in the supergravity theory also solve the four-derivative equations of motion. These results are then applied to explicitly calculate the regularized on-shell action for any asymptotically locally AdS4 solution of the two-derivative equations of motion. The four-derivative terms in the supergravity Lagrangian modify the entropy and other thermodynamic observables for the black hole solutions of the theory. We calculate these corrections explicitly and demonstrate that the quantum statistical relation holds for general stationary black holes in the presence of the four-derivative corrections. Employing an embedding of this supergravity model in M-theory we show how to use supersymmetric localization results in the holographically dual three-dimensional SCFT to determine the unknown coefficients in the four-derivative supergravity action. This in turn leads to new detailed results for the first subleading $$ {N}^{\frac{1}{2}} $$ N 1 2 correction to the large N partition function of a class of three-dimensional SCFTs on compact Euclidean manifolds. In addition, we calculate explicitly the first subleading correction to the Bekenstein-Hawking entropy of asymptotically AdS4 black holes in M-theory. We also discuss how to add matter multiplets to the supergravity theory in the presence of four-derivative terms and to generalize some of these results to six- and higher-derivative supergravity.

α′-corrections to near extremal dyonic strings and weak gravity conjecture

“…It should be interesting to explore further in the future in other setups with string theory embedding and see if similar features appear. After all, certain higher derivative extensions of supergravity models with string theory origin are also known in D = 4, 5 [33,34].…”

Factorization of log-corrections in AdS4/CFT3 from supergravity localization

“…• Put in a more general perspective, our work gives a better low-dimensional understanding of the underlying gravitational structure of log-corrections. Together with the results of [12,13] for the classical on-shell action and the results of [37,39,40] for the perturbative corrections arising from higher-derivative terms, our work makes progress in understanding the bulk structure of the effective four-dimensional theory. It is interesting and desirable to push this program further to higher-order loops by harvesting the full power of exact holography.…”

“…trary 6 perturbative corrections to the on-shell action of the background M 4 (see [37][38][39][40]). We will also show that the form of our one-loop result is valid, at leading order holographically, for any supersymmetric field content, making our formula applicable to a completely arbitrary set of supermultiplets that might not even be known at present.…”

Wrapped M5-branes and complex saddle points

“…The expression (4.41) has been obtained by reducing eleven-dimensional supergravity. However, it is also possible to obtain the higher-derivative correction to four-dimensional supergravity, as done in [10], and compare the results. Their expression for the Euclidean action including four-derivative corrections is…”

“…One of the far-reaching properties of the formula for the on-shell action is that we don't need the analytic form of the metric, which is generally quite difficult to find, but rather only knowledge of the topology of Y 4 and of the circle action generated by ξ. This poses conceptual problems, such as suggesting the existence of an underlying fixed point theorem acting on the supergravity background, especially given that this localization persists also for corrections to the two-derivative model [10][11][12], and it also applies to complex metrics [13]. More concretely, it provides a way of computing the on-shell action of any smooth solution, assuming its existence.…”