Solutions Of String Theory Research Articles

A NAKED SINGULARITY STABLE UNDER SCALAR FIELD PERTURBATIONS

We prove the stability of a spacetime with a naked singularity under scalar field perturbations, where the perturbations are regular at the singularity. This spacetime, found by Janis, Newman and Winicour and independently by Wyman, is sourced by a massless scalar field and also arises as a certain limit of a class of charged dilatonic solutions in string theory. This stability result opens up specific questions for investigation related to the cosmic censorship conjecture and the mechanism by which it is implemented in nature.

Lifshitz metric with hyperscaling violation from NS5-Dp states in string theory

In previous papers Dey and Roy (2012) [1,2] we have shown how Lifshitz-like space–time (space–time having a Lifshitz scaling along with a hyperscaling violation) can arise by taking near horizon limits of certain intersecting solutions (F-string with Dp-branes and also with two D-branes) of string theory. In this Letter we construct intersecting bound state solutions in the form of NS5-Dp-branes (with 1⩽p⩽6) of type II string theories. These are 1/4 BPS and threshold bound states unlike the known NS5-Dp bound states which are 1/2 BPS and non-threshold. We show that the near horizon limits of these solutions also lead to Lifshitz-like space–time with the dynamical scaling exponent z=0 and the hyperscaling violation exponent θ=9−p. The spatial dimension of the boundary theory is d=7−p. The dilatons in these theories are not constant in general (except for p=5) and therefore produce RG flows. So, we also consider the strong coupling phases of these theories and find that these phases also have similar Lifshitz-like structures, except for p=2, where it has an AdS3 structure.

Black holes and black strings of N = 2, d = 5 supergravity in the H-FGK formalism

We study general classes and properties of extremal and non-extremal static black-hole solutions of N = 2, d = 5 supergravity coupled to vector multiplets using the recently proposed H-FGK formalism, which we also extend to static black strings. We explain how to determine the integration constants and physical parameters of the blackhole and black-string solutions. We derive some model-independent statements, including the transformation of non-extremal flow equations to the form of those for the extremal flow. We apply our methods to the construction of example solutions (among others a new extremal string solution of heterotic string theory on K 3 × S 1). In the cases where we have calculated it explicitly, the product of areas of the inner and outer horizon of a non-extremal solution coincides with the square of the moduli-independent area of the horizon of the extremal solution with the same charges.

On some exact solutions in p-adic open-closed string theory

The paper is concerned with the construction of exact solutions for nonlinear pseudodifferential equations which describe tachyon dynamics of open-closed p-adic strings. Existence of continuous solutions and their properties are discussed.

Constructing Lifshitz solutions from AdS

Under general assumptions, we show that a gravitational theory in d + 1 dimensions admitting an AdS solution can be reduced to a d-dimensional theory containing a Lifshitz solution with dynamical exponent z = 2. Working in a d = 4, \( \mathcal{N} = 2 \) supergravity setup, we prove that if the AdS background is \( \mathcal{N} = 2 \) supersymmetric, then the Lifshitz geometry preserves 1/4 of the supercharges, and we construct the corresponding Killing spinors. We illustrate these results in examples from supersymmetric consistent truncations of type IIB supergravity, enhancing the class of known 4-dimensional Lifshitz solutions of string theory. As a byproduct, we find a new AdS4 × S 1 × T 1,1 solution of type IIB.

Gross-Neveu models, nonlinear Dirac equations, surfaces and strings

Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. These (static) condensates can be found analytically because the relevant Hartree-Fock and gap equations can be reduced to the nonlinear Schr\"odinger equation, whose deformations are governed by the mKdV and AKNS integrable hierarchies, respectively. Recently, Thies et al have shown that time-dependent Hartree-Fock solutions describing baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation, and can be mapped directly to classical string solutions in AdS3. Here we propose a geometric perspective for this result, based on the generalized Weierstrass spinor representation for the embedding of 2d surfaces into 3d spaces, which explains why these well-known integrable systems underlie these various Gross-Neveu gap equations, and why there should be a connection to classical string theory solutions. This geometric viewpoint may be useful for higher dimensional models, where the relevant integrable hierarchies include the Davey-Stewartson and Novikov-Veselov systems.

Lifshitz solutions in supergravity and string theory

We derive Lifshitz configurations in string theory for general dynamical exponents z ≥ 1. We begin by obtaining simple Li × Ω solutions to supergravities in diverse dimensions, with Ω a compact constant curvature manifold. Then we uplift the solutions to ten dimensions, providing configurations that correspond to warped compactifications in Type II string theory.

Cosmological intersecting brane solutions in string theory

The recent discovery of an explicit dynamical description of p-branes makes it possible to investigate the existence of intersection of such objects. We generalize the solutions depending on the overall transverse space coordinates and time to those which depend also on the relative transverse space and satisfy new intersection rules. We give classification of these dynamical intersecting brane solutions involving two branes, and discuss the application of these solutions to cosmology and show that these give Friedmann–Lemaitre–Robertson–Walker cosmological solutions.

String theory and the real world

Although string theory is formulated in 10 or 11 dimensions, specific string theory solutions make unambiguous, testable predictions about our four-dimensional universe.

State-space correlations and stabilities

The state-space pair correlation functions and notion of stability of extremal and non-extremal black holes in string theory and M-theory are considered from the viewpoints of thermodynamic Ruppeiner geometry. From the perspective of intrinsic Riemannian geometry, the stability properties of these black branes are divulged from the positivity of principle minors of the space-state metric tensor. We have explicitly analyzed the state-space configurations for (i) the two and three charge extremal black holes, (ii) the four and six charge non-extremal black branes, which both arise from the string theory solutions. An extension is considered for the $D_6$-$D_4$-$D_2$-$D_0$ multi-centered black branes, fractional small black branes and two charge rotating fuzzy rings in the setup of Mathur's fuzzball configurations. The state-space pair correlations and nature of stabilities have been investigated for three charged bubbling black brane foams, and thereby the M-theory solutions are brought into the present consideration. In the case of extremal black brane configurations, we have pointed out that the ratio of diagonal space-state correlations varies as inverse square of the chosen parameters, while the off diagonal components vary as inverse of the chosen parameters. We discuss the significance of this observation for the non-extremal black brane configurations, and find similar conclusion that the state-space correlations extenuate as the chosen parameters are increased.

Wilson loops in string duals of walking and flavored systems

We consider the VEV of Wilson loop operators by studying the behavior of string probes in solutions of Type IIB string theory generated by Nc D5 branes wrapped on an internal manifold. In particular, we focus on solutions to the background equations that are dual to field theories with a walking gauge coupling as well as for flavored systems. We present in detail our walking solution and emphasize various general aspects of the procedure to study Wilson loops using string duals. We discuss the special features that the strings show when probing the region associated with the walking of the field theory coupling.

Quantum critical superconductors in string theory and M-theory

We construct zero-temperature solutions of supergravity theories in five and four dimensions which interpolate between two copies of anti-de Sitter space, one of which preserves an Abelian gauge symmetry while the other breaks it. These domain wall solutions can be lifted to solutions of type IIB string theory and eleven-dimensional supergravity. They describe quantum critical behavior and emergent relativistic conformal symmetry in a superfluid or superconducting state of a strongly coupled dual gauge theory. We include computations of frequency-dependent conductivities which exhibit power law scaling in the infrared, with exponents determined by irrelevant perturbations to the symmetry-breaking anti-de Sitter background.

Black hole solutions in string theory with Gauss-Bonnet curvature correction

We present the black hole solutions and analyse their properties in the superstring effective field theory with the Gauss-Bonnet curvature correction terms. We find qualitative differences in our results from those obtained in the truncated model in the Einstein frame. The main difference in our model from the truncated one is that the existence of a turning point in the mass-area curve, the mass-entropy curve, and the mass-temperature curve in five and higher dimensions, where we expect a change of stability. We also find a mass gap in our model, where there is no black hole solution. In five dimensions, there exists a maximum black hole temperature and the temperature vanishes at the minimum mass, which is not found in the truncated model.

Non chiral dynamical flavors and screening on the conifold

AbstractWe present a new class of string theory solutions which are conjectured to be dual to the 𝒩 = 1 conifold theory by Klebanov and Witten coupled to non chiral massive dynamical flavors. These are introduced, in the Veneziano limit, by means of suitably embedded and smeared D7‐branes whose full backreaction on the background is taken into account. The string solutions are used to study chromoelectric charge screening effects due to the dynamical flavors in the non perturbative regime of the dual gauge theories.

Non-supersymmetric D1/D5, F/NS5 and closed string tachyon condensation

We construct the intersecting non-supersymmetric (non-susy) D1/D5 solution of type IIB string theory. While, as usual, the solution is charged under an electric two-form and an electric six-form gauge field, it also contains a non-susy chargeless (non-BPS) D0-brane. The S-dual of this solution is the non-susy F/NS5 solution. We show how these solutions nicely interpolate between the corresponding black (or non-extremal) solutions and the Kaluza–Klein (KK) “bubble of nothing” (BON) by continuously changing some parameters characterizing the solutions from one set of values to another. We show, by a time symmetric general bubble initial data analysis, that the final bubbles in these cases are static and stable and the interpolations can be physically interpreted as closed string tachyon condensation. As special cases, we recover the transition of two charge black F-string to BON, considered by Horowitz, and also the transition from AdS 3 black hole to global AdS 3.

AdS3 × w(S3 × S3 × S1) solutions of type IIB string theory

We analyse a recently constructed class of local solutions of type IIB supergravity that consist of a warped product of AdS3 with a seven-dimensional internal space. In one duality frame the only other non-vanishing fields are the NS 3-form and the dilaton. We analyse in detail how these local solutions can be extended to give infinite families of globally well-defined solutions of type IIB string theory, with the internal space having topology S3 × S3 × S1 and with properly quantized 3-form flux.

Obstacle to populating the string theory landscape

We construct domain walls and instantons in a class of models with coupled scalar fields, determining, in agreement with previous studies, that many such solutions contain naked timelike singularities. Vacuum bubble solutions of this type do not contain a region of true vacuum, obstructing the ability of eternal inflation to populate other vacua. We determine a criterion that potentials must satisfy to avoid the existence of such singularities and show that many domain wall solutions in type IIB string theory are singular.

Wilson loops in 3-dimensional 𝒩 = 6 supersymmetric Chern-Simons theory and their string theory duals

We study Wilson loops in the three-dimensional N=6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena, that is conjectured to be dual to type IIA string theory on AdS_4 x CP^3. We construct loop operators in the Chern-Simons theory which preserve 1/6 of the supercharges and calculate their expectation value up to 2-loop order at weak coupling. The expectation value at strong coupling is found by constructing the string theory duals of these operators. For low dimensional representations these are fundamental strings, for high dimensional representations these are D2-branes and D6-branes. In support of this identification we demonstrate that these string theory solutions match the symmetries, charges and the preserved supersymmetries of their Chern-Simons theory counterparts.

Exact wave solutions to 6D gauged chiral supergravity

We describe a broad class of time-dependent exact wave solutions to 6D gauged chiral supergravity with two compact dimensions. These 6D solutions are nontrivial warped generalizations of 4D pp-waves and Kundt class solutions and describe how a broad class of previously-static compactifications from 6D to 4D (sourced by two 3-branes) respond to waves moving along one of the uncompactified directions. Because our methods are generally applicable to any higher dimensional supergravity they are likely to be of use for finding the supergravity limit of time-dependent solutions in string theory. The 6D solutions are interesting in their own right, describing 6D shock waves induced by high energy particles on the branes, and as descriptions of the near-brane limit of the transient wavefront arising from a local bubble-nucleation event on one of the branes, such as might occur if a tension-changing phase transition were to occur.

BLACK HOLE BOUND STATES AND THEIR QUANTIZATION

We briefly review the construction of multi-centered black hole solutions in type IIA string theory. We then discuss a decoupling limit which embeds these solutions in M-theory on AdS 3 × S 2 × CY , and discuss some aspects of their dual CFT interpretation. Finally, we consider the quantization of these solutions and applications to the wall-crossing formula and the "fuzzball" proposal.