We revisit the computation of logarithmic corrections to black holes with N ≥ 2 supersymmetry. We employ an on-shell method that takes advantage of the symmetries in the AdS 2 × S 2 near horizon geometry. For bulk modes interactions are incorporated through the spectrum of chiral primaries that we derive afresh. The spectrum of boundary states is computed explicitly by analyzing gauge variations. Elementary heat kernels in 4Dand 2D then give the logarithmic corrections to the black hole entropy. Our computation represents a streamlined and simplified derivation that agrees with the results recently found by A. Sen.

We compute the off-shell spectrum of supergravity on AdS 2 × S 2 by explicit diagonalization of the equations of motion for an effective AdS 2 theory where all fields are dualized to scalars and spin-1 2 fermions. We classify all bulk modes as physical, gauge violating, and pure gauge then compute the physical spectrum by explicit cancellation of unphysical modes. We identify boundary modes as physical fields on S 2 that are formally pure gauge but with gauge function that is non-normalizable on AdS 2 . As an application we compute the leading quantum correction to AdS 2 × S 2 as a sum over physical fields including boundary states. The result agrees with a previous computation by Sen [1] where unphysical modes were canceled by ghosts.

Recently, a non-relativistic off-shell formulation of three dimensional NewtonCartan supergravity was proposed as the c → ∞ limit of three dimensional N = 2 supergravity [1]. In the present paper we study supersymmetric backgrounds within this theory. Using integrability constraints for the non-relativistic Killing spinor equations, we explicitly construct all maximally supersymmetric solutions, which admit four supercharges. In addition to these solutions, there are 1 2 -BPS solutions with reduced supersymmetry. We give explicit examples of such backgrounds and derive necessary conditions for backgrounds preserving two supercharges. Finally, we address how supersymmetric backgrounds of N = 2 supergravity are connected to the solutions found here in the c → ∞ limit.

We reconsider the one loop divergence of N = 8 supergravity in four dimensions. We compute the finite effective potential of N = 8 anti-deSitter supergravity and interpret it as logarithmic running of the cosmological constant. We show that quantum inequivalence between fields that are classically dual is due to boundary modes in AdS 4 . The boundary modes are important in global AdS 4 but not in thermal AdS 4 since these geometries have different Euler characteristic.

Abstract:We extend the results of [1], computing one loop partition functions for massive fields with spin half in AdS 2 using the quasinormal mode method proposed by Denef, Hartnoll, and Sachdev [2]. We find the finite representations of SO(2, 1) for spin zero and spin half, consisting of a highest weight state |h and descendants with non-unitary values of h. These finite representations capture the poles and zeroes of the one loop determinants. Together with the asymptotic behavior of the partition functions (which can be easily computed using a large mass heat kernel expansion), these are sufficient to determine the full answer for the one loop determinants. We also discuss extensions to higher dimensional AdS 2n and higher spins.