Duality Symmetry and the Cardy Limit

We study supersymmetric and non-supersymmetric extremal black holes obtained in Type IIA string theory compactified on K3 X T^2, with duality group O(6,22,Z) X SL(2,Z). In the Cardy limit an internal circle combines with the AdS_2 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.Comment: 46 pages, Latex, Some comments added in Introduction and Conclusions. Minor changes made in sections 3.4 and

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 CP^4. Working in the mirror IIB description we find non-supersymmetric attractors near the Gepner point.Comment: Added a few clarification

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.Comment: 21 pages, revised version contains a new appendix on dimensional reduction of spinors and some changes in the spinor equation

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 T^6/Z_2, six of the sixteen zero modes originally present are lifted by the flux.Comment: Important factor of ``i'' was overlooked in Euclidean continuation of WZ term. This changes the count of zero-modes in the T^6/Z_2 example. Main result stays unchanged. We thank Bergshoeff, Kallosh, Kashani-Poor, Sorokin and Tomasiello for pointing this ou

Non-Supersymmetric Stringy Attractors

In this paper we examine the stability of non-supersymmetric attractors in type IIA supergravity compactified on a Calabi-Yau manifold, in the presence of sub-leading corrections to the N=$ pre-potential. We study black hole configurations carrying D0-D6 and D0-D4 charges. We consider the O(1) corrections to the pre-potential given by the Euler number of the Calabi-Yau manifold. We argue that such corrections in general can not lift the zero modes for the D0-D6 attractors. However, for the attractors carrying the D0-D4 charges, they affect the zero modes in the vector multiplet sector. We show that, in the presence of such O(1) corrections, the D0-D4 attractors can either be stable or unstable depending on the geometry of the underlying Calabi-Yau manifold, and on the specific values of the charges they carry.Comment: corrected typos, minor modification

Instanton Corrected Non-Supersymmetric Attractors

We discuss non-supersymmetric attractors with an instanton correction in Type IIA string theory compactified on a Calabi-Yau three-fold at large volume. For a stable non-supersymmetric black hole, the attractor point must minimize the effective black hole potential. We study the supersymmetric as well as non-supersymmetric attractors for the D0-D4 system with instanton corrections. We show that in simple models, like the STU model, the flat directions of the mass matrix can be lifted by a suitable choice of the instanton parameters.Comment: Minor modifications, Corrected typos, 38 pages, 1 figur

Gaugino Condensation and Nonperturbative Superpotentials in Flux Compactifications

There are two known sources of nonperturbative superpotentials for K\"ahler moduli in type 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 first class of effects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the fourfold, is relatively well understood. The second class has been less explored. In this paper, we consider the explicit example of F-theory on $K3 \times K3$ with flux. The fluxes lift the D7 brane matter fields, and stabilize stacks of D7 branes at loci of enhanced gauge symmetry. The resulting theories exhibit gaugino condensation, and generate a nonperturbative superpotential for K\"ahler moduli. We describe how the relevant geometries in general contain cycles of arithmetic genus $\chi \geq 1$ (and how $\chi > 1$ divisors can contribute to the superpotential, in the presence of flux). This second class of effects is likely to be important in finding even larger classes of models where the KKLT mechanism of moduli stabilization can be realized. We also address various claims about the situation for IIB models with a single K\"ahler modulus.Comment: 24 pages, harvmac, no figures, references adde

Self-dual Maxwell Chern-Simons Solitons In 1+1 Dimensions

We study the domain wall soliton solutions in the relativistic self-dual Maxwell Chern-Simons model in 1+1 dimensions obtained by the dimensional reduction of the 2+1 model. Both topological and nontopological self-dual solutions are found in this case. A la BPS dyons here the Bogomol'ny bound on the energy is expressed in terms of two conserved quantities. We discuss the underlying supersymmetry. Nonrelativistic limit of this model is also considered and static, nonrelativistic self-dual soliton solutions are obtained.Comment: 18 pages RevTex, 2 figures included, to appear in Phys. Rev.

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.Comment: 20 pages, Late

Compactification with Flux on K3 and Tori

We study compactifications of Type IIB string theory on a K3 \times T^2/Z_2 orientifold in the presence of RR and NS flux. We find the most general supersymmetry preserving, Poincare invariant, vacua in this model. All the complex structure moduli and some of the Kahler moduli are stabilised in these vacua. We obtain in an explicit fashion the restrictions imposed by supersymmetry on the flux, and the values of the fixed moduli. Some T-duals and Heterotic duals are also discussed, these are non-Calabi-Yau spaces. A superpotential is constructed describing these duals.Comment: Discussion of susy breaking vacua significantly altere