Solutions Of String Theory Research Articles

Janus within Janus

We found a simple and interesting generalization of the non-supersymmetric Janus solution in type IIB string theory. The Janus solution can be thought of as a thick AdS_d-sliced domain wall in AdS_{d+1} space. It turns out that the AdS_d-sliced domain wall can support its own AdS_{d-1}-sliced domain wall within it. Indeed this pattern persists further until it reaches the AdS_2-slice of the domain wall within self-similar AdS_{p (2<p\le d)}-sliced domain walls. In other words the solution represents a sequence of little Janus nested in the interface of the parent Janus according to a remarkably simple ``nesting'' rule. Via the AdS/CFT duality, the dual gauge theory description is in general an interface CFT of higher codimensions.

Global properties of an exact string theory solution in two and four dimensions

This paper discusses global properties of exact (in � ′ ) string theory solutions: A deformed black hole solution in two dimensions and a Taub-NUT type solution in four dimensions. These models are exact by virtue of having CFT descriptions in terms of heterotic coset models. The analysis includes analytic continuations of the metric, motion of test particles, and the T-duality which acts as a map between different regions of the extended solutions, rendering the physical spacetimes non-singular.

Iterative method for solving nonlinear integral equations describing rolling solutions in string theory

We consider a nonlinear integral equation with infinitely many derivatives that appears when a system of interacting open and closed strings is investigated if the nonlocality in the closed string sector is neglected. We investigate the properties of this equation, construct an iterative method for solving it, and prove that the method converges.

Comparison of approaches to quantum correction of black hole thermodynamics

There are several approaches to quantum gravitational corrections of black hole thermodynamics. String theory and loop quantum gravity, by direct analysis on the basis of quantum properties of black holes, show that in the entropy–area relation the leading order correction should be of log-area type. On the other hand, generalized uncertainty principle (GUP) and modified dispersion relations (MDRs) provide perturbational framework for such modifications. Although both GUP and MDRs are common features of all quantum gravity scenarios, their functional forms are quantum gravity model dependent. Since both string theory and loop quantum gravity give more reliable solution of the black hole thermodynamics, one can use their results to test approximate results of GUP and MDRs. In this Letter, we find quantum corrected black hole thermodynamics in the framework of GUP and MDR and then we compare our results with string theory solutions. This comparison suggests severe constraints on the functional form of GUP and MDRs. These constraints may reflect characteristic features of ultimate quantum gravity theory.

A matrix model for the null-brane

The null-brane background is a simple smooth 1/2 BPS solution of string theory. By tuning a parameter, this background develops a big crunch/big bang type singularity. We construct the DLCQ description of this space-time in terms of a Yang-Mills theory on a time-dependent space-time. Our dual Matrix description provides a non-perturbative framework in which the fate of both (null) time, and the string S-matrix can be studied.

Ppwave big bangs: Matrix strings and shrinking fuzzy spheres

We find pp wave solutions in string theory with null-like linear dilatons. These provide toy models of big bang cosmologies. We formulate Matrix String Theory in these backgrounds. Near the big bang ``singularity'', the string theory becomes strongly coupled but the Yang-Mills description of the matrix string is weakly coupled. The presence of a second length scale allows us to focus on a specific class of non-abelian configurations, viz. fuzzy cylinders, for a suitable regime of parameters. We show that, for a class of pp waves, fuzzy cylinders which start out big at early times dynamically shrink into usual strings at sufficiently late times.

Chern-Simons theory and topological strings

A review of the relation between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces is given. This relation has made it possible to give an exact solution of topological string theory on these spaces to all orders in the string coupling constant. Here the focus is on the construction of this solution, which is encoded in the topological vertex, and the implications of the physics of string/gauge theory duality for knot theory and for the geometry of Calabi-Yau manifolds.

New instability for rotating black branes and strings

The evolution of small perturbations around rotating black branes and strings, which are low energy solutions of string theory, are investigated. For simplicity, we concentrate on the Kerr solution times transverse flat extra dimensions, possibly compactified, but one can also treat other branes composed of any rotating black hole and extra transverse dimensions, as well as analogue black hole models and rotating bodies in fluid mechanics systems. It is shown that such a rotating black brane is unstable against any massless (scalar, vectorial, tensorial or other) field perturbation for a wide range of wavelengths and frequencies in the transverse dimensions. Since it holds for any massless field it can be considered, in this sense, a stronger instability than the one studied by Gregory and Laflamme. Accordingly, it has also a totally different physical origin. The perturbations can be stabilized if the extra dimensions are compactified to a length smaller than the minimum wavelength for which the instability settles in, resembling in this connection the Gregory–Laflamme case. Likewise, this instability will have no effect for astrophysical black holes. However, in the large extra dimensions scenario, where TeV scale black holes can be produced, this instability should be important. It seems plausible that the endpoint of this instability is a static, or very slowly rotating, black brane and some outgoing radiation at infinity.

CURRENT TRENDS IN STRING THEORY

This article is a short survey of some of the recent ideas and techniques employed in string theory and M–theory towards the goal of understanding our universe. It is by no means exhaustive, and the vast majority of the article has an emphasis on the development of ideas pertaining to realizing our universe as a solution of string (and M–) theory, and to cosmological matters.

BPS pp-wave brane cosmological solutions in string theory

We construct time dependent BPS pp-wave brane solutions in the context of M-theory and type II supergravity. It is found that N-brane solutions we considered satisfy the crossing rule as S-brane solutions but 1/8 supersymmetry remains. By applying them to the cosmological setting, inflationary solutions are obtained. During this inflation, the size of the extradimensions becomes smaller than our four-dimensional spacetime dynamically. We also discuss the mechanism for terminating this inflation and recovering the hot big-bang universe.

Rotating solutions of non-relativistic string theory

We construct classical rotating solutions of non-relativistic string theory. The relation among the energy and angular momenta for these solutions is of the type E = J 2 . Some of the solutions saturate a BPS bound for the energy, they are 1 4 BPS supersymmetric configurations.

Exact geometry of a Kerr-Taub-NUT solution of string theory

In this paper we study a solution of heterotic string theory corresponding to a rotating Kerr-Taub-NUT spacetime. It has an exact CFT description as a heterotic coset model, and a Lagrangian formulation as a gauged WZNW model. It is a generalisation of a recently discussed stringy Taub-NUT solution, and is interesting as another laboratory for studying the fate of closed timelike curves and cosmological singularities in string theory. We extend the computation of the exact metric and dilaton to this rotating case, and then discuss some properties of the metric, with particular emphasis on the curvature singularities.

Colliding Plane Wave Solutions in String theory Revisited

We construct the colliding plane wave solutions in the higher-dimensional gravity theory with fluxes and dilaton, with a more general ansatz on the metric. We consider two classes of solutions to the equations of motions and after imposing the junction conditions we find that they are all physically acceptable. In particular, we manage to obtain the higher-dimensional Bell-Szekeres solutions in the Maxwell-Einstein gravity theory, and the flux-CPW solutions in the eleven-dimensional supergravity theory. All the solutions have been shown to develop the late time curvature singularity.

Closed strings in Misner space: stringy fuzziness with a twist

Misner space, also known as the Lorentzian orbifold , is the simplest tree-level solution of string theory with a cosmological singularity. Wecompute tree-level scattering amplitudes involving twisted states, using operatorand current algebra techniques. We find that, due to zero-point quantumfluctuations of the excited modes, twisted strings with a large winding numberw are fuzzy on a scale , which can be much larger than the string scale. Wavefunctions are smeared by anoperator reminiscent of the Moyal product of non-commutative geometry, which, sinceΔ(ν) is real, modulates the amplitude rather than the phase of the wavefunction, and is purelygravitational in its origin. We compute the scattering amplitude of two twisted states and onetachyon or graviton, and find a finite result. The scattering amplitude of two twisted andtwo untwisted states is found to diverge, due to the propagation of intermediate windingstrings with vanishing boost momentum. The scattering amplitude of three twisted fields iscomputed by analytic continuation from three-point amplitudes of states with non-zerop+ in the Nappi–Witten plane wave, and the non-locality of the three-point vertexis found to diverge for certain kinematical configurations. Our results for thethree-point amplitudes allow us in principle to compute, to leading order, theback-reaction on the metric due to a condensation of coherent winding strings.

Is there a string theory landscape?

We examine recent claims of a large set of flux compactification solutions of string theory. We conclude that the arguments for AdS solutions are plausible. The analysis of meta-stable dS solutions inevitably leads to situations where long distance effective field theory breaks down. We then examine whether these solutions are likely to lead to a description of the real world. We conclude that one must invoke a version of the anthropic principle which insists on carbon based life forms. We explain why it is likely that this leads to a prediction of low energy supersymmetry breaking, but that many features of anthropically selected flux compactifications are likely to disagree with experiment.

Traversable Lorentzian wormholes in the vacuum low energy effective string theory in Einstein and Jordan frames

Three new classes (II-IV) of solutions of the vacuum low energy effective string theory in four dimensions are derived. Wormhole solutions are investigated in those solutions including the class I case both in the Einstein and in the Jordan (string) frame. It turns out that, of the eight classes of solutions investigated (four in the Einstein frame and four in the corresponding string frame), massive Lorentzian traversable wormholes exist in five classes. Nontrivial massless limit exists only in class I Einstein frame solution while none at all exists in the string frame. An investigation of test scalar charge motion in the class I solution in the two frames is carried out by using the Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski-Sawicki theorem. A curious consequence is that the motion around the extremal zero (Keplerian) mass configuration leads, as a result of scalar-scalar interaction, to a new hypothetical ``mass'' that confines test scalar charges in bound orbits, but does not interact with neutral test particles.

The geometry of fractional D1-branes

We find explicit solutions of type IIB string theory on corresponding to the classical geometry of fractional D1-branes. From the supergravity solution obtained, we capture perturbative information about the running of the coupling constant and the metric on the moduli space of super Yang–Mills.

Caustic Formation in Tachyon Effective Field Theories

Certain configurations of D-branes, for example wrong dimensional branes or the brane-antibrane system, are unstable to decay. This instability is described by the appearance of a tachyonic mode in the spectrum of open strings ending on the brane(s). The decay of these unstable systems is described by the rolling of the tachyon field from the unstable maximum to the minimum of its potential. We analytically study the dynamics of the inhomogeneous tachyon field as it rolls towards the true vacuum of the theory in the context of several different tachyon effective actions. We find that the vacuum dynamics of these theories is remarkably similar and in particular we show that in all cases the tachyon field forms caustics where second and higher derivatives of the field blow up. The formation of caustics signals a pathology in the evolution since each of the effective actions considered is not reliable in the vicinity of a caustic. We speculate that the formation of caustics is an artifact of truncating the tachyon action, which should contain all orders of derivatives acting on the field, to a finite number of derivatives. Finally, we consider inhomogeneous solutions in p-adic string theory, a toy model of the bosonic tachyon which contains derivatives of all orders acting on the field. For a large class of initial conditions we conclusively show that the evolution is well behaved in this case. It is unclear if these caustics are a genuine prediction of string theory or not.

Gravitational waves in string theory in anti-de Sitter background

Inspired by the studies of gravitational waves in anti-de Sitter universe, in general relativity, in this Letter we investigate the possibility of similar solutions in IIB string theory on AdS3×S3×R4. We give a general form for such solutions in this background and present several explicit examples, by directly solving the field equations, as well as the ones obtained by taking a scaling limit on D1–D5 brane systems in a pp-wave background. The form of the metric in our solutions corresponds to a gravitational wave in AdS3. We show the supersymmetric nature of these solutions and discuss the possibility of their generalizations to other anti-de Sitter backgrounds, including the ones in four dimensions.

Rolling tachyon solution of two-dimensional string theory

We consider a classical (string) field theory of $c=1$ matrix model which was developed earlier in hep-th/9207011 and subsequent papers. This is a noncommutative field theory where the noncommutativity parameter is the string coupling $g_s$. We construct a classical solution of this field theory and show that it describes the complete time history of the recently found rolling tachyon on an unstable D0 brane.