We study the behaviour of extremal and near-extremal black holes at low energies and low temperat... more We study the behaviour of extremal and near-extremal black holes at low energies and low temperatures and find that it can be understood from the near-horizon AdS 2 region. Our analysis includes charged matter and also goes beyond the S-wave approximation. We find that the leading behaviour at low energies arises from a mode linked to time reparametrisations and from phase modes arising from gauge fields. At somewhat higher energies, additional modes arising from higher partial waves can also be cumulatively significant. These results can be applied quite generally to cases where an AdS 2 × S d near-horizon geometry arises, including black holes in asymptotically AdS and flat space-times.
We find examples of non-supersymmetric attractors in Type II string theory compactified on a Cala... more We find examples of non-supersymmetric attractors in Type II string theory compactified on a Calabi Yau threefold. 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.
We derive the fermion bilinear terms in the world volume action for a D3 brane in the presence of... more 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 nonperturbative corrections to the superpotential can arise from an Euclidean D3brane 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.
Journal of Cosmology and Astroparticle Physics, Oct 30, 2003
We investigate the embedding of brane inflation into stable compactifications of string theory. A... more We investigate the embedding of brane inflation into stable compactifications of string theory. At first sight a warped compactification geometry seems to produce a naturally flat inflaton potential, evading one well-known difficulty of brane-antibrane scenarios. Careful consideration of the closed string moduli reveals a further obstacle: superpotential stabilization of the compactification volume typically modifies the inflaton potential and renders it too steep for inflation. We discuss the non-generic conditions under which this problem does not arise. We conclude that brane inflation models can only work if restrictive assumptions about the method of volume stabilization, the warping of the internal space, and the source of inflationary energy are satisfied. We argue that this may not be a real problem, given the large range of available fluxes and background geometries in string theory.
It has been suggested in arXiv:2004.00613 that in Dp-brane holography, entanglement in the target... more It has been suggested in arXiv:2004.00613 that in Dp-brane holography, entanglement in the target space of the D-brane Yang-Mills theory provides a precise notion of bulk entanglement in the gravity dual. We expand on this discussion by providing a gauge invariant characterization of operator sub-algebras corresponding to such entanglement. This is achieved by finding a projection operator which imposes a constraint characterizing the target space region of interest. By considering probe branes in the Coloumb branch we provide motivation for why the operator sub-algebras we consider are appropriate for describing a class of measurements carried out with low-energy probes in the corresponding bulk region of interest. We derive expressions for the corresponding Renyi entropies in terms of path integrals which can be directly used in numerical calculations.
We study supersymmetric and non-supersymmetric extremal black holes obtained in Type IIA string t... more We study supersymmetric and non-supersymmetric extremal black holes obtained in Type IIA string theory compactified on K3 × T 2 , with duality group O(6, 22, Z) × 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.
We consider a system consisting of a strongly interacting, ultracold unitary Fermi gas under harm... more We consider a system consisting of a strongly interacting, ultracold unitary Fermi gas under harmonic confinement. Our analysis suggests the possibility of experimentally studying, in this system, an anisotropic shear viscosity tensor driven by the anisotropy in the trapping potential. In particular, we suggest that this experimental setup could mimic some features of anisotropic geometries that have recently been studied for strongly coupled field theories which have a gravitational dual. Results using the AdS/CFT correspondence in these theories show that in systems with a background linear potential, certain viscosity components can be made much smaller than the entropy density, parametrically violating the bound proposed by Kovtun, Son and Starinets (KSS). This intuition, along with results from a Boltzmann analysis that we perform, suggests that a violation of the KSS bound can perhaps occur in the unitary Fermi gas system when it is subjected to a suitable anisotropic trapping potential which may be approximated to be linear in a suitable range of parameters. We give a concrete proposal for an experimental setup where an anisotropic shear viscosity tensor may arise. In such situations, it may also be possible to observe a reduction in the spin one component of the shear viscosity from its lowest value observed so far in ultracold Fermi gases. In extreme anisotropic situations, the reduction may be enough to reduce the shear viscosity to entropy ratio below the proposed KSS bound, although this regime is difficult to analyze in a theoretically controlled manner.
The presence of RR and NS three-form fluxes in type IIB string compactification on a Calabi-Yau o... more 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 N = 1 supersymmetric no-scale supergravity, including some nonsupersymmetric solutions with relatively small values of W. Our examples arise on orientifolds of the hypersurfaces in W P 4 1,1,1,1,4 and W P 4 1,1,2,2,6. 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.
We consider theories with gravity, gauge fields and scalars in four-dimensional asymptotically fl... more We consider theories with gravity, gauge fields and scalars in four-dimensional asymptotically flat space-time. By studying the equations of motion directly we show that the attractor mechanism can work for non-supersymmetric extremal black holes. Two conditions are sufficient for this, they are conveniently stated in terms of an effective potential involving the scalars and the charges carried by the black hole. Our analysis applies to black holes in theories with N 1 supersymmetry, as well as non-supersymmetric black holes in theories with N = 2 supersymmetry. Similar results are also obtained for extremal black holes in asymptotically Anti-de Sitter space and in higher dimensions.
At zero temperature the Coulomb Branch of N = 4 super Yang-Mills theory is described in supergrav... more At zero temperature the Coulomb Branch of N = 4 super Yang-Mills theory is described in supergravity by multi-center solutions with D3-brane charge. At finite temperature and chemical potential the vacuum degeneracy is lifted, and minima of the free energy are shown to have a supergravity description as rotating black D3-branes. In the extreme limit these solutions single out preferred points on the moduli space that can be interpreted as simple distributions of branes-for instance, a uniformly charged planar disc. We exploit this geometrical representation to study the thermodynamics of rotating black D3-branes. The low energy excitations of the system appear to be governed by an effective string theory which is related to the singularity in spacetime.
Recently, a relation between N = 4 Super Yang Mills in 3+1 dimensions and supergravity in an AdS ... more Recently, a relation between N = 4 Super Yang Mills in 3+1 dimensions and supergravity in an AdS 5 background has been proposed. In this paper we explore the idea that the correspondence between operators in the Yang Mills theory and modes of the supergravity theory can be obtained by using the D3 brane action. Specifically, we consider two form gauge fields for this purpose. The supergravity analysis predicts that the operator which corresponds to this mode has dimension six. We show that this is indeed the leading operator in the three brane Dirac-Born-Infeld and Wess-Zumino action which couples to this mode. It is important in the analysis that the brane action is expanded around the anti de-Sitter background. Also, the Wess-Zumino term plays a crucial role in cancelling a lower dimension operator which appears in the the Dirac-Born-Infeld action.
In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic v... more In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic vector matter. In particular we present an exact calculation of the free energy of the N = 2 supersymmetric model (with one chiral field) for all values of the 't Hooft coupling in the large N limit. This is done by using a generalization of the standard Hubbard-Stratanovich method because the SUSY model contains higher order polynomial interactions.
We find examples of non-supersymmetric attractors in Type II string theory compactified on a Cala... more We find examples of non-supersymmetric attractors in Type II string theory compactified on a Calabi Yau threefold. 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.
We study novel type IIB compactifications on the T 6 /Z 2 orientifold. This geometry arises in th... more We study novel type IIB compactifications on the T 6 /Z 2 orientifold. This geometry arises in the T-dual description of Type I theory on T 6 , and one normally introduces 16 space-filling D3-branes to cancel the RR tadpoles. Here, we cancel the RR tadpoles either partially or fully by turning on three-form flux in the compact geometry. The resulting (super)potential for moduli is calculable. We demonstrate that one can find many examples of N = 1 supersymmetric vacua with greatly reduced numbers of moduli in this system. A few examples with N > 1 supersymmetry or complete supersymmetry breaking are also discussed.
We describe a new class of supersymmetric string compactifications to 4d Minkowski space. These s... more We describe a new class of supersymmetric string compactifications to 4d Minkowski space. These solutions involve type II strings propagating on (orientifolds of) non Calabi-Yau spaces in the presence of background NS and RR fluxes. The simplest examples have descriptions as cosets, generalizing the three-dimensional nilmanifold. They can also be thought of as twisted tori. We derive a formula for the (super)potential governing the light fields, which is generated by the fluxes and certain "twists" in the geometry. Detailed consideration of an example also gives strong evidence that in some cases, these exotic geometries are related by smooth transitions to standard Calabi-Yau or G 2 compactifications of M-theory.
Due to the attractor mechanism, the entropy of an extremal black hole does not vary continuously ... more Due to the attractor mechanism, the entropy of an extremal black hole does not vary continuously as we vary the asymptotic values of various moduli fields. Using this fact we argue that the entropy of an extremal black hole in string theory, calculated for a range of values of the asymptotic moduli for which the microscopic theory is strongly coupled, should match the statistical entropy of the same system calculated for a range of values of the asymptotic moduli for which the microscopic theory is weakly coupled. This argument does not rely on supersymmetry and applies equally well to nonsupersymmetric extremal black holes. We discuss several examples which support this argument and also several caveats which could invalidate this argument.
We consider theories with gravity, gauge fields and scalars in four-dimensional asymptotically fl... more We consider theories with gravity, gauge fields and scalars in four-dimensional asymptotically flat space-time. By studying the equations of motion directly we show that the attractor mechanism can work for non-supersymmetric extremal black holes. Two conditions are sufficient for this, they are conveniently stated in terms of an effective potential involving the scalars and the charges carried by the black hole. Our analysis applies to black holes in theories with N 1 supersymmetry, as well as non-supersymmetric black holes in theories with N = 2 supersymmetry. Similar results are also obtained for extremal black holes in asymptotically Anti-de Sitter space and in higher dimensions.
We study supersymmetric and non-supersymmetric extremal black holes obtained in Type IIA string t... more We study supersymmetric and non-supersymmetric extremal black holes obtained in Type IIA string theory compactified on K3 × T 2 , with duality group O(6, 22, Z) × 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.
We study compactifications of Type IIB string theory on a K3 × T 2 /Z 2 orientifold in the presen... more We study compactifications of Type IIB string theory on a K3 × 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 Kähler 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.
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Papers by sandip trivedi