String Frame Research Articles

Small black holes in the large D limit

The large D limit of AdS2 × S D−2 solutions in the particular higher-derivative Lovelock-type theory is analyzed. The theory and the solutions were originally considered in an attempt to effectively describe near-horizon behavior of D-dimensional spherically symmetric 2-charge small extremal black holes which in superstring theory context are assumed to correspond to configurations in S 1 × T 9−D compactification schemes in which fundamental string is wound around circle S 1. Though in D → ∞ limit the action contains infinite number of higher-derivative terms, their contributions to equations of motion sum into simple exponential form which allows us to find explicit solutions. A simplicity of this example gives us the opportunity to study some connections between α′ and 1/D expansions. In the leading order in 1/D the relation between the string parameter α′ and the radius of the horizon r h (in the string frame) satisfies r h ∝ $ D\sqrt{{\alpha \prime }} $ , i.e., we obtain an explicit realization of the relation inferred by Emparan et al. in the different context of large black holes in the ordinary Einstein gravity where α′ is not manifestly present.

Late time acceleration of the 3-space in a higher dimensional steady state universe in dilaton gravity

We present cosmological solutions for (1+3+n)-dimensional steady state universe in dilaton gravity with an arbitrary dilaton coupling constant w and exponential dilaton self-interaction potentials in the string frame. We focus particularly on the class in which the 3-space expands with a time varying deceleration parameter. We discuss the number of the internal dimensions and the value of the dilaton coupling constant to determine the cases that are consistent with the observed universe and the primordial nucleosynthesis. The 3-space starts with a decelerated expansion rate and evolves into accelerated expansion phase subject to the values of w and n, but ends with a Big Rip in all cases. We discuss the cosmological evolution in further detail for the cases w = 1 and w = ½ that permit exact solutions. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the internal dimensions and thinks that the conventional general relativity is valid at cosmological scales.

T-duality of the Riemann curvature corrections to supergravity

We examine the sigma model Riemann curvature corrections to the supergravity action under T-duality transformations. Using the compatibility of the effective action with on-shell linear T-duality and with the S-matrix calculations as guiding principles, we have incorporated in this action the couplings of four B-field strengths and the couplings of two Riemann curvatures and two B-field strengths at order α′3. Using the S-matrix calculations we have also found new dilaton couplings in the string frame at this order.

Conformal Relativity versus Brans–Dicke and Superstring Theories

We show how conformal relativity is related to Brans–Dicke theory and to low-energy-effective superstring theory. Conformal relativity or the Hoyle–Narlikar theory is invariant with respect to conformal transformations of the metric. We show that the conformal relativity action is equivalent to the transformed Brans–Dicke action for ω = -3/2 (which is the border between standard scalar field and ghost) in contrast to the reduced (graviton-dilaton) low-energy-effective superstring action which corresponds to the Brans–Dicke action with ω = -1. We show that like in ekpyrotic/cyclic models, the transition through the singularity in conformal cosmology in the string frame takes place in the weak coupling regime. We also find interesting self-duality and duality relations for the graviton-dilaton actions.

Accelerating universes in string theory via field redefinition

We study cosmological solutions in the effective heterotic string theory with α′-correction terms in the string frame. It is pointed out that the effective theory has an ambiguity via field redefinition and we analyze generalized effective theories due to this ambiguity. We restrict our analysis to the effective theories which give equations of motion of second order in the derivatives, just as “Galileon” field theory. This class of effective actions contains two free coupling constants. We find de Sitter solutions as well as the power-law expanding universes in our four-dimensional Einstein frame. The accelerated expanding universes are always attractors in the present dynamical system.

Null geodesics of charged black holes in string theory

In this paper, we investigate the null geodesics of the static charged black hole in heterotic string theory. A detailed analysis of the geodesics are done in the Einstein frame as well as in the string frame. In the Einstein frame, the geodesics are solved exactly in terms of the Jacobi-elliptic integrals for all possible energy levels and angular momentum of the photons. In the string frame, the geodesics are presented for the circular orbits. As a physical application of the null geodesics, we have obtained the angle of deflection for the photons and the quasinormal modes of a massless scalar field in the eikonal limit.

GEOMETRIC IIA SUPERGRAVITY THEORIES IN THE STRING FRAME

Using the geometric (rheonomic) approach based on the Free Differential Algebra, we derive the full type IIA D = 10 supergravity Lagrangian in the string frame, including the Romans' mass deformation, and containing the explicit four-fermion interactions, absent from the original Romans' paper. This provides a deeper insight into the group theoretical and algebraic structures of the theory. Moreover we provide the full set of supersymmetry transformation laws both in the Romans'-deformed and undeformed theories. The structure of the bosonic Free Differential Algebra for the HLW deformation is also presented.

Two-charge rotating black holes in four-dimensional gauged supergravity

We obtain an asymptotically AdS, non-extremal, electrically charged and rotating black hole solution of four-dimensional U(1)4 gauged supergravity with two non-zero and independent U(1) charges. The thermodynamical quantities are computed. We find BPS solutions that are nakedly singular. The solution is generalized to include a NUT parameter and dyonic gauge fields. The string frame metric has a rank-2 Killing–Stäckel tensor and has completely integrable geodesic motion, and the massless Klein–Gordon equation separates for the Einstein frame metric.

AdS black hole solutions in dilatonic Einstein-Gauss-Bonnet gravity

We find that anti--de Sitter (AdS) spacetime with a nontrivial linear dilaton field is an exact solution in the effective action of the string theory, which is described by gravity with the Gauss-Bonnet curvature terms coupled to a dilaton field in the string frame without a cosmological constant. The AdS radius is determined by the spacetime dimensions and the coupling constants of curvature corrections. We also construct the asymptotically AdS black hole solutions with a linear dilaton field numerically. We find these AdS black holes for hyperbolic topology and in dimensions higher than four. We discuss the thermodynamical properties of those solutions. Extending the model to the case with the even-order higher Lovelock curvature terms, we also find the exact AdS spacetime with a nontrivial dilaton. We further find a cosmological solution with a bounce of three-dimensional space and a solitonic solution with a nontrivial dilaton field, which is regular everywhere and approaches an asymptotically AdS spacetime.

Chameleonic dilaton, nonequivalent frames, and the cosmological constant problem in quantum string theory

The chameleonic behavior of the string theory dilaton is suggested. Some of the possible consequences of the chameleonic string dilaton are analyzed in detail. In particular, (1) we suggest a new stringy solution to the cosmological constant problem and (2) we point out the nonequivalence of different conformal frames at the quantum level. In order to obtain these results, we start taking into account the (strong coupling) string loop expansion in the string frame (S-frame), therefore the so-called form factors are present in the effective action. The correct dark energy scale is recovered in the Einstein frame (E-frame) without unnatural fine-tunings and this result is robust against all quantum corrections, granted that we assume a proper structure of the S-frame form factors in the strong coupling regime. At this stage, the possibility still exists that a certain amount of fine-tuning may be required to satisfy some phenomenological constraints. Moreover in the E-frame, in our proposal, all the interactions are switched off on cosmological length scales (i.e., the theory is IR-free), while higher derivative gravitational terms might be present locally (on short distances) and it remains to be seen whether these facts clash with phenomenology. A detailed phenomenological analysis is definitely necessary to clarify these points.

Bouncing universe and non-BPS branes

We describe string frame bouncing universe scenarios involving the creation and annihilation of a non-BPS D9-brane in type IIA superstring theory. We find several classes of solutions, in which the bounce is driven by the tachyon dynamics of the non-BPS brane. The metric and dilaton during the bounce are consistently described in terms of the lowest order effective action. The bounce solutions interpolate between contracting and expanding pre-big bang (or post-big bang) solutions. The singular behavior of our bounce solutions is the same as that of the pre-big bang (or post-big bang) solution.

Wrapped brane gas as a candidate for dark matter

We consider brane gas models based on type II string theories and analyze the mass, the Ramond-Ramond charge and the charge on moduli fluctuations of branes wrapping over cycles of a compactified space in the four-dimensional Einstein frame. A six-dimensional torus and Calabi-Yau threefolds are considered for the Kaluza-Klein reduction. A large volume of the compactified space and a weak string coupling gives rise to point particles of the wrapped branes which have a light mass and a small charge of the Ramond-Ramond flux and of the moduli fluctuations, while the particles become very heavy in the string frame. We find that the masses and the charges satisfy the sea-saw like dual relations which become time-independent in the four-dimensional Einstein frame.

The Cosmological Slingshot Scenario in details

We generalize the Cosmological Slingshot Scenario for a Slingshot brane moving in a Klebanov-Strassler throat. We show that the horizon and isotropy problems of standard cosmology are avoided, while the flatness problem is acceptably alleviated. Regarding the primordial perturbations, we identify their vacuum state and elucidate the evolution from the quantum to the classical regimes. Also, we calculate their exact power spectrum showing its compatibility with current data. We discuss the bouncing solution from a four dimensional point of view. In this framework the radial and angular motion of the Slingshot brane are described by two scalar fields. We show that the bouncing solution for the scale factor in String frame is mapped into a monotonically increasing (in conformal time) solution in the Einstein frame. We finally discuss about the regularity of the geometry in Einstein frame.

New spin(7) holonomy metrics admittingG2holonomy reductions and M-theory/type-IIA dualities

As is well known, when D6 branes wrap a special Lagrangian cycle on a noncompact Calabi-Yau threefold in such a way that the internal string frame metric is a Kaehler one there exists a dual description, which is given in terms of a purely geometrical 11-dimensional background with an internal metric of G{sub 2} holonomy. It is also known that when D6 branes wrap a coassociative cycle of a noncompact G{sub 2} manifold in the presence of a self-dual two-form strength the internal part of the string frame metric is conformal to the G{sub 2} metric and there exists a dual description, which is expressed in terms of a purely geometrical 11-dimensional background with an internal noncompact metric of spin(7) holonomy. In the present work it is shown that any G{sub 2} metric participating in the first of these dualities necessarily participates in one of the second type. Additionally, several explicit spin(7) holonomy metrics admitting a G{sub 2} holonomy reduction along one isometry are constructed. These metrics can be described as R fibrations over a 6-dimensional Kaehler metric, thus realizing the pattern spin(7){yields}G{sub 2}{yields}(Kahler) mentioned above. Several of these examples are further described as fibrations over the Eguchi-Hanson gravitational instantonmore » and, to the best of our knowledge, have not been previously considered in the literature.« less

Curvature-corrected dilatonic black holes and black hole—string transition

We investigate extremal charged black hole solutions in the four-dimensional string frame Gauss-Bonnet gravity with the Maxwell field and the dilaton. Without curvature corrections, the extremal electrically charged dilatonic black holes have singular horizon and zero Bekenstein entropy. When the Gauss-Bonnet term is switched on, the horizon radius expands to a finite value provided curvature corrections are strong enough. Below a certain threshold value of the Gauss-Bonnet coupling the extremal black hole solutions cease to exist. Since decreasing Gauss-Bonnet coupling corresponds to decreasing string coupling $g_s$, the situation can tentatively be interpreted as classical indication on the black hole -- string transition. Previously the extremal dilaton black holes were studied in the Einstein-frame version of the Gauss-Bonnet gravity. Here we work in the string frame version of this theory with the S-duality symmetric dilaton function as required by the heterotic string theory.

Open strings on D-branes and Hagedorn regime in string gas cosmology

We consider early time cosmic evolution in string gas cosmology dominated by open strings attached to D-branes. After reviewing statistical properties of open strings in D-brane backgrounds, we use dilaton-gravity equations to determine the string frame fields. Although, there are distinctions in the Hagedorn regime thermodynamics and dilaton coupling as compared to closed strings, it seems difficult to avoid Jeans instability and assume thermal equilibrium simultaneously, which is already a known problem for closed strings. We also examine characteristics of a possible subsequent large radius regime in this setup.

Pure spinor superstrings on generic type IIA supergravity backgrounds

We derive the Free Differential Algebra for type IIA supergravity in 10 dimensions in the string frame. We provide all fermionic terms for all curvatures. We derive the Green-Schwarz sigma model for type IIA superstring based on the FDA construction and we check its invariance under κ-symmetry. Finally, we derive the pure spinor sigma model and we check the BRST invariance. The present derivation has the advantage that the resulting sigma model is constructed in terms of the superfields appearing in the FDA and therefore one can directly relate a supergravity background with the corresponding sigma model. The complete explicit form of the BRST transformations is given and some new pure spinor constraints are obtained. Finally, the explicit form of the action is given.

Graceful exit via polymerization of pre-big-bang cosmology

We consider a phenomenological modification of the pre-big-bang scenario using ideas from the resolution of curvature singularities in loop quantum cosmology. We show that nonperturbative loop modifications to the dynamics, arising from the underlying polymer representation, can resolve the graceful exit problem. The curvature and the dilaton energy stay finite at all times, in both the string and Einstein frames. In the string frame, the dilaton tends to a constant value at late times after the bounce.

Viscous hydrodynamics relaxation time from AdS/CFT correspondence

We consider an expanding boost-invariant plasma at strong coupling using the AdS/CFT correspondence for $\mathcal{N}=4$ super Yang-Mills theory. We determine the relaxation time in second order viscous hydrodynamics and find that it is around 30 times shorter than weak coupling expectations. We find that the nonsingularity of the dual geometry in the string frame necessitates turning on the dilaton which leads to a nonvanishing expectation value for $\mathrm{tr}{F}^{2}$ behaving like ${\ensuremath{\tau}}^{\ensuremath{-}10/3}$.

Graviton propagators in supergravity and noncommutative gauge theory

We investigate the graviton propagator in the type IIB supergravity background which is dual to 4 dimensional noncommutative gauge theory. We assume that the boundary is located not at the infinity but at the noncommutative scale where the string frame metric exhibits the maximum. We argue that the Neumann boundary condition is the appropriate boundary condition to be adopted at the boundary. We find that the graviton propagator behaves just as that of the 4 dimensional massless graviton. On the other hand, the non-analytic behaviors of the other Kaluza-Klein modes are not significantly affected by the Neumann boundary condition.