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

We use the Atiyah-Singer index theorem to derive the general form of the one-loop corrections to observables in asymptotically anti-de Sitter (AdS4) supersymmetric backgrounds of abelian gauged supergravity. Using the method of supergravity localization combined with the factorization of the supergravity action on fixed points (NUTs) and fixed two-manifolds (Bolts) we show that an analogous factorization takes place for the one-loop determinants of supergravity fields. This allows us to propose a general fixed-point formula for the logarithmic corrections to a large class of supersymmetric partition functions in the large N expansion of a given 3d dual theory. The corrections are uniquely fixed by some simple topological data pertaining to a particular background in the form of its regularized Euler characteristic χ, together with a single dynamical coefficient that counts the underlying degrees of freedom of the theory.

Optimal Effort on Self-Insurance-Cum-Protection: A New Analysis Using Yaari’s Dual Theory

People take different measures to control risks. The measures that can simultaneously reduce loss probability and loss size are called self-insurance-cum-protection. This paper studies self-insurance-cum-protection using Yaari’s dual theory. We analyze the comparative statics of increased risk aversion. Two different sufficient conditions are found in the two-state model, from which an increase in the level of risk aversion will lead to an increase in the level of self-insurance-cum-protection. The first condition is a new result under Yaari’s dual theory and its implication is that the more risk-averse individual is willing to exert greater effort on self-insurance-cum-protection if the probability of loss can be reduced to very small by a less risk-averse individual with optimal effort. The second condition depends on the forms of the self-insurance-cum protection cost and the loss. This condition is the same as that obtained under expected utility in existing literature. Our study therefore assures the robustness this result. We also study comparative statics in the continuous model and find out that the results are analogous to that in the two-state model. In addition, we consider how the availability of market insurance affects the self-insurance-cum-protection level. When the probability of loss is small, the self-insurance-cum-protection and market insurance are substitutes. This means when market insurance is available, people tend to exert less effort on self-insurance-cum-protection.

De Sitter entropy as holographic entanglement entropy

We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newton's constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.

Wiedemann-Franz laws and Sl(2, ℤ) duality in AdS/CMT holographic duals and one-dimensional effective actions for them

In this paper we study the Wiedemann-Franz laws for transport in 2+1 dimensions, and the action of Sl(2, ℤ) on this transport, for theories with an AdS/CMT dual. We find that Sl(2, ℤ) restricts the RG-like flow of conductivities and that the Wiedemann-Franz law is $$ \overline{L}=\overline{\kappa}/\left( T\sigma \right)={cg}_4^2\uppi /3 $$ L ¯ = κ ¯ / Tσ = cg 4 2 π / 3 , from the weakly coupled gravity dual. In a self-dual theory this value is also the value of L = κ/(Tσ) in the weakly coupled field theory description. Using the formalism of a 0+1 dimensional effective action for both generalized SY Kq models and the AdS4 gravity dual, we calculate the transport coefficients and show how they can be matched at large q. We construct a generalization of this effective action that is invariant under Sl(2, ℤ) and can describe vortex conduction and integer quantum Hall effect.

New non-extremal and BPS hairy black holes in gauged $$ \mathcal{N} $$ = 2 and $$ \mathcal{N} $$ = 8 supergravity

In this article we study a family of four-dimensional, $$ \mathcal{N} $$ N = 2 supergravity theories that interpolates between all the single dilaton truncations of the SO(8) gauged $$ \mathcal{N} $$ N = 8 supergravity. In this infinitely many theories characterized by two real numbers — the interpolation parameter and the dyonic “angle” of the gauging — we construct non-extremal electrically or magnetically charged black hole solutions and their supersymmetric limits. All the supersymmetric black holes have non-singular horizons with spherical, hyperbolic or planar topology. Some of these supersymmetric and non-extremal black holes are new examples in the $$ \mathcal{N} $$ N = 8 theory that do not belong to the STU model. We compute the asymptotic charges, thermodynamics and boundary conditions of these black holes and show that all of them, except one, introduce a triple trace deformation in the dual theory.

F-theory superspace

We consider, at the linearized level, the superspace formulation of lower-dimensional F-theory. In particular, we describe the embedding of 3D Type II super-gravity of the superstring, or 4D, N = 1 supergravity of M-theory, into the corresponding F-theory in full detail, giving the linearized action and gauge transformations in terms of the prepotential. This manifestly supersymmetric formulation reveals some features not evident from a component treatment, such as Weyl and local S-supersymmetry invariances. The linearized multiplet appears as a super 3-form (just as that for the manifestly T-dual theory is a super 2-form), reflecting the embedding of M-theory (as the T-dual theory embeds Type II supergravity). We also give the embedding of matter multiplets into this superspace, and derive the F-constraint from the gauge invariance of the gauge invariance.