A new class of N = 2 locally supersymmetric higher-derivative invariants is constructed based on logarithms of conformal primary chiral superfields. They characteristically involve a coupling to R µν 2 − 1 3 R 2 , which equals the non-conformal part of the GaussBonnet term. Upon combining one such invariant with the known supersymmetric version of the square of the Weyl tensor one obtains the supersymmetric extension of the Gauss-Bonnet term. The construction is carried out in the context of both conformal superspace and the superconformal multiplet calculus. The new class of supersymmetric invariants resolves two open questions. The first concerns the proper identification of the 4D supersymmetric invariants that arise from dimensional reduction of the 5D mixed gauge-gravitational Chern-Simons term. The second is why the pure Gauss-Bonnet term without supersymmetric completion has reproduced the correct result in calculations of the BPS black hole entropy in certain models.

We study N " p2, 4, 8q supersymmetric extensions of the three dimensional BMS algebra (BMS 3 ) with most generic possible central extensions. We find that N-extended supersymmetric BMS 3 algebras can be derived by a suitable contraction of two copies of the extended superconformal algebras. Extended algebras from all the consistent contractions are obtained by scaling left-moving and right-moving supersymmetry generators symmetrically, while Virasoro and R-symmetry generators are scaled asymmetrically. On the way, we find that the BMS/GCA correspondence does not in general hold for supersymmetric systems. Using the β-γ and the b-c systems, we construct free field realisations of all the extended super-BMS 3 algebras.

Abstract:We consider two possible flat space limits of three dimensional N = (1, 1) AdS supergravity. They differ by how the supercharges are scaled with the AdS radius ℓ: the first limit (democratic) leads to the usual super-Poincaré theory, while a novel 'twisted' theory of supergravity stems from the second (despotic) limit. We then propose boundary conditions such that the asymptotic symmetry algebras at null infinity correspond to supersymmetric extensions of the BMS algebras previously derived in connection to non-and ultra-relativistic limits of the N = (1, 1) Virasoro algebra in two dimensions. Finally, we study the supersymmetric energy bounds and find the explicit form of the asymptotic and global Killing spinors of supersymmetric solutions in both flat space supergravity theories.

We analyze BPS black hole attractors in the conformal 4d gauged supergravity formalism and apply the technique known as supergravity localization in order to evaluate Sen's quantum entropy function [1] in the AdS 2 ×S 2 near-horizon geometry. Under certain assumptions, we reduce the exact expression of the functional integral to a finite-dimensional integral for a number of supersymmetric black holes in gauged supergravity with AdS asymptotics subject to a holographic description via a dual field theory. Examples include the asymptotically AdS 4 ×S 7 Cacciatori-Klemm black holes [2] in Mtheory and the asymptotically AdS 5 ×S 5 generalizations of Gutowski-Reall black holes [3] and Benini-Bobev black strings [4] in type IIB, as well as the recently constructed asymptotically AdS 4 ×S 6 solutions [5,6] in massive type IIA. Our results provide an important first step towards a gravitational counterpart to the exact evaluation of supersymmetric partition functions at finite N for the holographically dual field theories in these examples. arXiv:1803.05920v2 [hep-th]

Abstract:The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific fivedimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed.