Unreasonable Effectiveness of Higher Derivative Supergravity in AdS4 Holography

Abstract

We study four-derivative corrections to four-dimensional N ¼ 2 minimal gauged supergravity controlled by two real constants. The solutions of the equations of motion in the two-derivative theory are not modified by the higher-derivative corrections. We use this to derive a general formula for the regularized on-shell action for any asymptotically locally AdS 4 solution of the theory and show how the higher-derivative corrections affect black hole thermodynamic quantities in a universal way. We employ our results in the context of holography to derive explicit expressions for the subleading corrections in the large N expansion of supersymmetric partition functions on various compact manifolds for a large class of three-dimensional SCFTs.

Squashing, mass, and holography for 3d sphere free energy

“…This relation implies infinite relations between derivatives of F (b; m I ) evaluated at m = 0, b = 1, such as the fact that all four derivatives can be written in terms of the six quantities listed in (1.2). For the N = 8 ABJ(M) theories, these relations allowed us to compute ∂ 4 b F (b; m I ) and ∂ 5 b F (b; m I ) to all orders in 1/N , which at sub-leading order match the prediction given in (1.3) from M-theory compactified on AdS 4 × S 7 /Z k and expanded to leading order beyond the supergravity limit [21]. Our results provide constraints at further orders in 1/N that will allow more higher derivative corrections to supergravity to be derived following the program outlined in [21].…”

“…The first higher derivative corrections, i.e. the four derivative terms, were recently derived in [21] for any minimal N = 2 gauged supergravity on AdS 4 in terms of two theory dependent coefficients. These coefficients were then fixed for the ABJ(M) M-theory dual at finite k using the large N results for F (1, 0) and the coefficient c T of the stress tensor two-point function, which was computed using ∂ 2 m ± F in [22].…”

“…These coefficients were then fixed for the ABJ(M) M-theory dual at finite k using the large N results for F (1, 0) and the coefficient c T of the stress tensor two-point function, which was computed using ∂ 2 m ± F in [22]. The free energy could then be computed on any asymptotically AdS 4 solution to sub-leading order in 1/N , which for the case of squashing gave [21]:…”

“…The further sub-leading powers of 1/N in our result will allow the coefficients of future higher derivative corrections to supergravity to be similarly fixed. Note that once these higher derivative terms are known, they can be used to compute gravity quantities on any asymptotically AdS 4 solution, not just that corresponding to squashing, and can even be used to compute thermodynamic quantities like higher derivative corrections to the the black hole entropy [21], which are much more difficult to compute directly from CFT using holography.…”

Gravitational Cardy limit and AdS black hole entropy

“…It was shown in [60] that the central charge of the near-horizon asymptotic Virasoro symmetry also gets modified in the gravity with higher-derivative terms, while the Frolov-Thorne temperature and the Cardy formula still hold. Other higher-derivative aspects of AdS 4 black holes were recently considered [61,62]. A tantalizing property of higher-derivative corrections in AdS 5 black holes was recently reported in [63], which showed that the leading α -correction is absent in the BPS limit.…”