Prasanta K. Tripathy

Non-supersymmetric attractors in string theory

We find examples of non-supersymmetric attractors in Type II string theory compactified on a Calabi Yau three-fold. For a non-supersymmetric attractor the fixed values to which the moduli are drawn at the horizon must minimise an effective potential. For Type IIA at large volume, we consider a configuration carrying D0, D2, D4 and D6 brane charge. When the D6 brane charge is zero, we find for some range of the other charges, that a non-supersymmetric attractor solution exists. When the D6 brane charge is non-zero, we find for some range of charges, a supersymmetry breaking extremum of the effective potential. Closer examination reveals though that it is not a minimum of the effective potential and hence the corresponding black hole solution is not an attractor. Away from large volume, we consider the specific case of the quintic in CP4. Working in the mirror IIB description we find non-supersymmetric attractors near the Gepner point.

Flux compactifications on Calabi-Yau threefolds

The presence of RR and NS three-form fluxes in type IIB string compactification on a Calabi-Yau orientifold gives rise to a nontrivial superpotential W for the dilaton and complex structure moduli. This superpotential is computable in terms of the period integrals of the Calabi-Yau manifold. In this paper, we present explicit examples of both supersymmetric and nonsupersymmetric solutions to the resulting 4d {Nu} = 1 supersymmetric no-scale supergravity, including some nonsupersymmetric solutions with relatively small values of W. Our examples arise on orientifolds of the hypersurfaces in WP{sub 1,1,1,1,4}{sup 4} and WP{sub 1,1,2,2,6}{sup 4}. They serve as explicit illustrations of several of the ingredients which have played a role in the recent proposals for constructing de Sitter vacua of string theory.

Gaugino Condensation and Nonperturbative Superpotentials in Flux Compactifications

Department of Physics and SLACStanford UniversityStanford, CA 94305/94309, USAThere are two known sources of nonperturbative superpotentials for Kahler moduli intype IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux:Euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The firstclass of effects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisorsof arithmetic genus 1 in the fourfold, is relatively well understood. The second class hasbeen less explored. In this paper, we consider the explicit example of F-theory on K3×K3with flux. The fluxes lift the D7 brane matter fields, and stabilize stacks of D7 branes atloci of enhanced gauge symmetry. The resulting theories exhibit gaugino condensation,and generate a nonperturbative superpotential for Kahler moduli. We describe how therelevant geometries in general contain cycles of arithmetic genus χ ≥ 1 (and how χ > 1divisors can contribute to the superpotential, in the presence of flux). This second class ofeffects is likely to be important in finding even larger classes of models where the KKLTmechanism of moduli stabilization can be realized. We also address various claims aboutthe situation for IIB models with a single Kahler modulus.July 2004

D3 brane action and fermion zero modes in presence of background flux

We derive the fermion bilinear terms in the world volume action for a D3 brane in the presence of background flux. In six-dimensional compactifications non-perturbative corrections to the superpotential can arise from an euclidean D3-brane instanton wrapping a divisor in the internal space. The bilinear terms give rise to fermion masses and are important in determining these corrections. We find that the three-form flux generically breaks a U(1) subgroup of the structure group of the normal bundle of the divisor. In an example of compactification on T6/Z2, twelve of the sixteen zero modes originally present are lifted by the flux.

On the stability of non-supersymmetric attractors in string theory

We study non-supersymmetric attractors obtained in Type IIA compactifications on Calabi Yau manifolds. Determining if an attractor is stable or unstable requires an algebraically complicated analysis in general. We show using group theoretic techniques that this analysis can be considerably simplified and can be reduced to solving a simple example like the STU model. For attractors with D0?D4 brane charges, determining stability requires expanding the effective potential to quartic order in the massless fields. We obtain the full set of these terms. For attractors with D0?D6 brane charges, we find that there is a moduli space of solutions and the resulting attractors are stable. Our analysis is restricted to the two derivative action.

Fermion Zero Modes in the Presence of Fluxes and a Non-perturbative Superpotential

We study the effect of background fluxes of general Hodge type on the supersymmetry conditions and on the fermionic zero modes on the world-volume of a Euclidean M5/D3-brane in M-theory/type IIB string theory. Using the naive susy variation of the modulino fields to determine the number of zero modes in the presence of a flux of general Hodge type, an inconsistency appears. This inconsistency is resolved by a modification of the supersymmetry variation of the modulinos, which captures the back-reaction of the non-perturbative effects on the background flux and the geometry.

Duality symmetry and the Cardy limit

We study supersymmetric and non-supersymmetric extremal black holes obtained in Type IIA string theory compactified on K3 ? T2, with duality group O(6,?22,?) ? SL(2,?). In the Cardy limit an internal circle combines with the AdS2 component in the near horizon geometry to give a BTZ black hole whose entropy is given by the Cardy formula. We study black holes carrying D0?D4 and D0?D6 brane charges. We find, both in the supersymmetric and non-supersymmetric cases, that a generic set of charges cannot be brought to the Cardy limit using the duality symmetries. In the non-supersymmetric case, unlike the supersymmetric one, we find that when the charges are large, a small fractional change in them always allows the charges to be taken to the Cardy limit. These results could lead to a microscopic determination of the entropy for extremal non-supersymmetric black holes, including rotating cases like the extreme Kerr black hole in four dimensions.

The Geroch group in Einstein spaces

Geroch?s solution-generating method is extended to the case of Einstein spaces, which possess a Killing vector and are thus asymptotically (locally) (anti) de Sitter. This includes the reduction to a three-dimensional coset space, the description of the dynamics in terms of a sigma-model and its transformation properties under the group, and the reconstruction of new four-dimensional Einstein spaces. The detailed analysis of the space of solutions is performed using the Hamilton?Jacobi method in the instance where the three-dimensional coset space is conformal to . The cosmological constant appears in this framework as a constant of motion and transforms under .

Generalized attractors in five-dimensional gauged supergravity

A bstractIn this paper we study generalized attractors in

Multiple Single-Centered Attractors

\mathcal{N} = 2