Swapna Mahapatra

Moduli and (un)attractor black hole thermodynamics

We investigate four-dimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars non-minimally coupled to gauge fields. In the non-extremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of black hole thermodynamics. In the extremal limit, the near horizon geometry is AdS2 × S2 and the entropy does not depend on the values of moduli at infinity. We discuss the attractor behaviour by using Sen’s entropy function formalism as well as the effective potential approach and their relation with the results previously obtained through special geometry method. We also argue that the attractor mechanism is at the basis of the matching between the microscopic and macroscopic entropies for the extremal non-BPS Kaluza–Klein black hole.

Black hole entropy functions and attractor equations

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N = 2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions.

Exploring the relation between 4D and 5D BPS solutions

Abstract Based on recent proposals linking four and five-dimensional BPS solutions, we discuss the explicit dictionary between general stationary 4D and 5D supersymmetric solutions in N = 2 supergravity theories with cubic prepotentials. All these solutions are completely determined in terms of the same set of harmonic functions and the same set of attractor equations. As an example, we discuss black holes and black rings in Godel–Taub-NUT spacetime. Then we consider corrections to the 4D solutions associated with more general prepotentials and comment on analogous corrections on the 5D side.

FROM TYPE IIA BLACK HOLES TO T-DUAL TYPE IIB D-INSTANTONS IN N = 2, D = 4 SUPERGRAVITY

We discuss the T-duality between the solutions of type 11A versus IIB superstrings compactified on Calabi-Yau threefolds. Within the context of the N = 2, D = 4 supergravity effective Lagrangian, the T-duality transformation is equivalently described by the c-map, which relates the special Kahler moduli space of the IIA N = 2 vector multiplets to the quaternionic moduli space of the N = 2 hyper multiplets on the type IIB side (and vice versa). Hence the T-duality, or c-map respectively, transforms the IIA black hole solutions, originating from even-dimensional IIA branes, of the special Kahler effective action, into IIB D-instanton solutions of the IIB quaternionic σ-model action, where the D-instantons can be obtained by compactifying odd 1113 D-branes on the internal Calabi-Yau space. We construct via this mapping a broad class of D-instanton solutions in four dimensions which are determined by a set of harmonic functions plus the underlying topological Calabi-Yau data.

Subleading and non-holomorphic corrections to N=2 BPS black hole entropy

BPS black hole degeneracies can be expressed in terms of an inverse Laplace transform of a partition function based on a mixed electric/magnetic ensemble, which involves a non-trivial integration measure. This measure has been evaluated for black holes with various degrees of supersymmetry and for N = 4 supersymmetric black holes all results agree. It generally receives contributions from non-holomorphic corrections. An explicit evaluation of these corrections in the context of the effective action of the FHSV model reveals that these are related to, but quantitatively different from, the non-holomorphic corrections to the topological string, indicating that the relation between the twisted partition functions of the latter and the effective action is more subtle than has so far been envisaged. The effective action result leads to a duality invariant BPS free energy and arguments are presented for the existence of consistent non-holomorphic deformations of special geometry that can account for these effects. A prediction is given for the measure based on semiclassical arguments for a class of N = 2 black holes. Furthermore an attempt is made to confront some of the results of this paper with a recent proposal for the microstate degeneracies of the STU model.

Intersecting 6-branes from new 7-manifolds with G(2) holonomy

We discuss a new family of metrics of 7-manifolds with G2 holonomy, which are 3 bundles over a quaternionic space. The metrics depend on five parameters and have two abelian isometries. Certain singularities of the G2 manifolds are related to fixed points of these isometries; there are two combinations of Killing vectors that possess co-dimension four fixed points which yield upon compactification only intersecting D6-branes if one also identifies two parameters. Two of the remaining parameters are quantized and we argue that they are related to the number of D6-branes, which appear in three stacks. We perform explicitly the reduction to the type IIA model.

Construction of physical states of non-trivial ghost number in c < 1 string theory

Starting from the Liouville null-vectors in theories of c < 1 matter coupled to 2D gravity, we describe a procedure to explicitly construct elements of the BRS cohomology of ghost number ± 1. A crucial step in the analysis concerns the existence of null-states in the Liouville Fock module, for which a general criterion is obtained. The physical states are shown to satisfy a set of “descent equations”, and we compute their two-point function on the sphere. Our results are illustrated by a number of examples.

The mixed black hole partition function for the STU model

We evaluate the mixed partition function for dyonic BPS black holes using the recently proposed degeneracy formula for the STU model. The result factorizes into the OSV mixed partition function times a proportionality factor. The latter is in agreement with the measure factor that was recently conjectured for a class of N = 2 black holes that contains the STU model.

De Sitter vacua from N=2 gauged supergravity

Typical de Sitter (dS) vacua of gauged supergravity correspond to saddle points of the potential and often the unstable mode runs into a singularity. We explore the possibility to obtain dS points where the unstable mode goes on both sides into a supersymmetric smooth vacuum. Within N = 2 gauged supergravity coupled to the universal hypermultiplet, we have found a potential which has two supersymmetric minima (one of them can be flat) and these are connected by a de Sitter saddle point. In order to obtain this potential by an abelian gauging, it was important to include the recently proposed quantum corrections to the universal hypermultiplet sector. Our results apply to four as well as five dimensional gauged supergravity theories.

Planetoid strings: Solutions and perturbations

A novel ansatz for solving the string equations of motion and constraints in generic curved backgrounds, namely the planetoid ansatz, was proposed recently by some authors. We construct several specific examples of planetoid strings in curved backgrounds which include Lorentzian wormholes, spherical Rindler spacetime and the (2 + 1)-dimensional black hole. A semiclassical quantization is performed and the Regge relations for the planetoids are obtained. The general equations for the study of small perturbations about these solutions are written down using the standard, covariant formalism. Applications to special cases such as those of planetoid strings in Minkowski and spherical Rindler spacetimes are also presented.