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} = 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}} 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.
Highlights
Supergravity theories that arise in the low-energy limit of string or M-theory provide an accessible arena on which to explore the dynamics of a UV complete theory of quantum gravity
We explore this in the context of our four-derivative supergravity model and calculate explicitly the HD corrections to black hole charges and thermodynamic potentials
We go on to show how the higher-derivative corrections to thermodynamic quantities are compatible with the quantum statistical relation, before moving on to discuss the relations of these results to some recent proposals related to the weak gravity conjecture
Summary
Supergravity theories that arise in the low-energy limit of string or M-theory provide an accessible arena on which to explore the dynamics of a UV complete theory of quantum gravity. By studying the linearized spectrum of excitations around the AdS4 vacuum of the theory it is possible to calculate the coefficient of the two-point function of the stress-energy tensor in the dual CFT which takes the simple form It is well-known that black hole thermodynamics is modified in the presence of HD corrections. The leading HD correction to 11d supergravity comes at the eight-derivative order and it is not known how to reduce these eight-derivative terms to four-dimensions for N = 2 AdS4 compactifications To break this impasse we employ the holographic dictionary and recent results on supersymmetric localization in 3d SCFTs. For concreteness we focus on 3d SCFTs arising on the world-volume of M2-branes in M-theory. In addition to deriving in detail all the results announced in [8] we present many new results that can be found in sections 2.3, 4.2, and 7
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