Tanwi Ghosh, Soumitra SenGupta
Using brick wall method the entropy of charged dilaton-axion black hole is determined for both asymptotically flat and non-flat cases. The entropy turns out to be proportional to the horizon area of the black hole confirming the Beckenstien, Hawking area-entropy formula for black holes. The leading order logarithmic corrections to the entropy are also derived for such black holes.
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We presented the proof of the positive mass theorem for black holes in Einstein-Maxwell axion-dilaton gravity being the low-energy limit of the heterotic string theory. We show that the total mass of a spacetime containing a black hole is greater or equal to the square root of the sum of squares of the adequate dilaton-electric and dilaton-axion charges.
We study axion-dilaton cosmologies derived from the low-energy string effective action. We present the classical homogeneous Friedmann-Robertson-Walker solutions and derive the semi-classical perturbation spectra in the dilaton, axion and moduli fields in the pre-Big Bang scenario. By constructing the unique S-duality invariant field perturbations for the axion and dilaton fields we derive S-duality invariant solutions, valid when the axion field is time-dependent as well as in a dilaton-vacuum cosmology. Whereas the dilaton and moduli fields have steep blue perturbation spectra (with spectral…
We complete our previous study of critical gravitational collapse in the axion-dilaton system by analysing the hyperbolic and parabolic ansätze. As could be expected, the corresponding Choptuik exponents in four-dimensions differ from the elliptic case.
We prove the uniqueness theorem for stationary axisymmetric black hole solution in Einstein-Maxwell-axion-dilaton gravity being the low-energy limit of the heterotic string theory. We consider both non-degenerate and extremal Kerr-Sen black hole solutions.
We construct the Komar integral for axion-dilaton gravity using Wald's formalism and momentum maps and we use it to derive a Smarr relation for stationary axion-dilaton black holes. While the Wald-Noether 2-form charge is not invariant under SL(2,R) electric-magnetic duality transformations because Wald's formalism does not account for magnetic charges and potentials, the Komar integral constructed with it turns out to be invariant and, in more general theories, it will be fully symplectic invariant. We check the Smarr formula obtained with the most general family of static axion-dilaton black…
We study the gravitational collapse of the axion-dilaton system suggested by type IIB string theory in dimensions ranging from four to ten. We extend previous analysis concerning the role played by the global SL(2,R) symmetry and we evaluate the Choptuik exponents in the elliptic case.
We proved that strictly stationary Einstein-Maxwell-axion-dilaton spacetime with negative cosmological constant could not support a nontrivial configuration of complex scalar fields. We considered the general case of the arbitrary number of U(1) gauge fields in the theory under consideration.
Under $SL(2,R)$ electric-magnetic duality transformations the Bogomolnyi bound of dilaton-axion black holes is known to be invariant. In this paper we show that this invariance corresponds to the covariance of the $N=4$ supersymmetry transformation rules and their parameters. In particular this implies that Killing spinors transform covariantly into Killing spinors. As an example, we work out completely the case of the largest known family of axion-dilaton black holes which is $SL(2,R)$-invariant, finding the Killing spinors with the announced properties.
Cosmologically active Brans-Dicke (or dilaton) scalar fields are generically ruled out by solar system tests of gravity unless their couplings to ordinary matter are much suppressed relative to gravitational strength, and this is a major hindrance when building realistic models of light dilatons coupled to matter. We propose a new mechanism for evading such bounds if matter also couples to a light axion, that exploits nonlinear target-space curvature interactions to qualitatively change how the fields respond to a gravitating source. We find that dilaton-matter couplings that would be excluded…
Avoiding the problem of the existence of asymptotically constant spinors satysfying certain differential equations on a non-compact hypersrface we presented the proof of positivity of the ADM and Bondi energy in Einstein-Maxwell axion-dilaton gravity. In our attitude spinor fields defining the enwergy need only be defined near infinity and there satysfying propagation equations.
The axion-dilaton string effective action is expressed in Einstein frame metric in a manifestly S-duality invariant form. It is shown that the moduli can be redefined to describe surface of a 2+1 dimensional pseudosphere. The classical cosmological solutions are of axion-dilaton are revisited. The Wheeler De Witt equation for the system is exactly solved and complete set of eigenfunctions are presented. The wave function factorizes and the one depending on the moduli is obtained by appealing to the underlying S-duality symmetry. Axion and dilaton parametrize the coset SU(1,1)/U(1), the S-duali…
We present a proof of the positivity of the Bondi energy in Einstein-Maxwell axion-dilaton gravity, being the low-energy limit of the heterotic string theory. We consider the spacelike hypersurface which asymptotically approaches a null cone and on which the equations of the theory under consideration are given. Next, we generalize the proof allowing the hypersurface having inner boundaries.
A $2p + 5$ parametric family of black holes is constructed in dilaton--axion gravity with $p$ vector fields using a holomorphic representation of U--duality in three dimensions. The metric of the non--extremal black holes has a Reissner--Nordström type structure and generically possesses an internal horizon. However in the extremal limit the generic solution exhibits a dilatonic type null singularity. Only in the case of the orthogonal electric and magnetic charges (if $p>1$) the extremal solution may have a non--singular event horizon.
The colliding plane wave metric discovered by Ferrari and Ibañez to be locally isometric to the interior of a Schwarzschild black hole is extended to the case of general axion-dilaton black holes. Because the transformation maps either black hole horizon to the focal plane of the colliding waves, this entire class of colliding plane wave spacetimes only suffers from the formation of spacetime singularities in the limits where the inner horizon itself is singular, which occur in the Schwarzschild and dilaton black hole limits. The supersymmetric limit corresponding to the extreme axion-dilaton …
In this paper we generalize the previous works to the case that the near-horizon dynamics of the Einstein-Dilaton-Axion theory can be governed by the incompressible Navier-Stokes equation via imposing the Petrov-like boundary condition on hypersurfaces in the non-relativistic and near-horizon limit. The dynamical shear viscosity $η$ of such dual horizon fluid in our scenario, which isotropically saturates the Kovtun-Son-Starinet (KSS) bound, is independent of both the dilaton field and axion field in that limit.
The Wheeler-De Witt equation of type IIB quantum string cosmology compactified with constant internal H-fluxes on a 6-torus, whose volume modulus is frozen, is solved under the WKB approximation. The spontaneous symmetry breaking of the S-duality group by H-fluxes is also examined.
Compactification of type IIB theory on torus, in the presence of fluxes, is considered. The reduced effective action is expressed in manifestly S-duality invariant form. Cosmological solutions of the model are discussed in several cases in the Pre-Big Bang scenario.
Stability of Axion-Dilaton Wormholes
本文研究了渐近平坦空间下欧几里得轴子-伸缩子虫洞的微扰稳定性，发现无质量虫洞始终稳定，而有质量伸缩子情形下具有最小势的解稳定且占主导，分岔分支则存在负模导致不稳定。
In the framework of the Einstein-Maxwell-axion-aether theory we establish the model, the Lagrangian of which contains the sin-type generalization of the term describing the axion-photon coupling, and the axionically induced cosine-type modification of the term attributed to the dilaton-photon interactions. The extension of the axion-dilaton-aether electrodynamics is inspired by the Jackson's idea concerning the internal symmetry of the equations of electromagnetism. The application of the extended theory to the anisotropic homogeneous cosmological model of the Bianchi-I type is considered. The…
A global O$(2,2)$ symmetry is found in the Brans-Dicke theory of gravity when the dilaton is coupled to axion and moduli fields. The symmetry is broken if a cosmological constant is introduced. Within the class of spatially homogeneous Bianchi cosmologies, only the type I and V models respect the symmetry. Isotropic cosmological solutions are found for arbitrary spatial curvature. In the region of parameter space relevant to the pre-big bang scenario, the interplay between the scalar fields results in a bouncing cosmology.
Mass angular momentum and charge inequalities for axisymmetric maximal time-symmetric initial data invariant under an action of U(1) group, in Einstein-Maxwell-axion-dilaton gravity being the low-energy limit of the heterotic string theory, is established. We assume that data set with two asymptotically flat regions is given on smooth simply connected manifold. We also pay attention to the area momentum charge inequalities for a closed orintabler two-dimensional spacelike surface embedded in the spacetime of the considered theory.
Static black holes of dilaton-axion gravity become singular in the extreme limit, which prevents a direct determination of their near-horizon geometry. This is addressed by first taking the near-horizon limit of extreme rotating NUT-less black holes, and then going to the static limit. The resulting four-dimensional geometry may be lifted to a Bertotti-Robinson-like solution of six-dimensional vacuum gravity, which also gives the near-horizon geometry of extreme Kaluza-Klein black holes in five dimensions.
We study generic Einstein-Maxwell-Kalb-Ramond-dilaton actions, and derive conditions under which they give rise to static, spherically symmetric black hole solutions. We obtain new asymptotically flat and non-flat black hole solutions which are in general electrically and magnetically charged. They have positive definite and finite quasi-local masses. Existing non-rotating black hole solutions (including those appearing in low energy string theory) are recovered in special limits.
Conformal symmetry is investigated within the context of axion-dilaton-modulus theory of gravity of Brans-Dicke-type. A distinction is made between general conformal symmetry and invariance under transformations of the physical units. The conformal degree of symmetry of the theory is studied when quantum fermion (lepton) modes with electromagnetic interaction are considered. Based on the requirement of invariance of the physical laws under general transformations of the units of measure, arguments are given that point at a matter action with non-minimal coupling of the dilaton to the matter fi…
Four--dimensional Einstein--Maxwell--dilaton--axion system restricted to space--times with one non--null Killing symmetry is formulated as the three--dimensional gravity coupled sigma--model. Several alternative representations are discussed and the associated hidden symmetries are revealed. The action of target space isometries on the initial set of (non--dualized ) variables is found. New mulicenter solutions are obtained via generating technique based on the formulation in terms of the non--dualized variables.
Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges associated with the asymptotic symmetry group is obtained. It is shown that the microscopic entropy of the dual conformal field given by Cardy formula exactly agrees with Bekenstein-Hawking entropy of extrema…
We construct charged black hole solutions with hyperscaling violation in the infrared(IR) region in Einstein-Maxwell-Dilaton-Axion theory and investigate the temperature behavior of the ratio of holographic shear viscosity to the entropy density. When translational symmetry breaking is relevant in the IR, the power law of the ratio is testified numerically at low temperature $T$, namely, $η/s\sim T^κ$, where the values of exponent $κ$ coincide with the analytical results. We also find that the exponent $κ$ is not affected by irrelevant current, but is reduced by the relevant current.
New stationary solutions of $4$-dimensional dilaton-axion gravity are presented, which correspond to the charged Taub-NUT and Israel-Wilson-Perjes (IWP) solutions of Einstein-Maxwell theory. The charged axion-dilaton Taub-NUT solutions are shown to have a number of interesting properties: i) manifest $SL(2,R)$ symmetry, ii) an infinite throat in an extremal limit, iii) the throat limit coincides with an exact CFT construction. The IWP solutions are shown to admit supersymmetric Killing spinors, when embedded in $d=4,N=4$ supergravity. This poses a problem for the interpretation of supersymmetr…
Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we derived the formulas for the variation of mass and other asymptotic conserved quantities in the theory under consideration. Generalizing this kind of reasoning to the initial dota for the manifold with an interior boundary we got the generalized first law of black hole mechanics. We consider an asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity describing a black hole with a Killing vector field timelike at infinity, the horizon of which comprises a bifurcate Killing horizon with a bifurcate surf…
The minimal Starobinsky supergravity with the inflaton (scalaron) and the goldstino in a massive vector supermultiplet is coupled to the dilaton-axion chiral superfield with the no-scale Kähler potential and a superpotential. The Kachru-Kallosh-Linde-Trivedi (KKLT)-type mechanism in the presence of a constant term in the superpotential is applied to stabilize the dilaton/axion during inflation, and it is shown to lead to an instability. The instability is cured by adding the alternative Fayet-Iliopoulos (FI) term that does not lead to the gauged $R$-symmetry. Other stabilization mechanisms, ba…
We derive general formulae for the first order variation of the ADM mass, angular momentum for linear perturbations of a stationary background in Einstein-Maxwell axion-dilaton gravity being the low-energy limit of the heterotic string theory. All these variations were expressed in terms of the perturbed matter energy momentum tensor and the perturbed charge current density. Combining these expressions we reached to the form of the {\it physical version} of the first law of black hole dynamics for the stationary black holes in the considered theory being the strong support for the cosmic censo…
A class of Einstein-dilaton-axion models is found for which almost all flat expanding homogeneous and isotropic universes undergo recurrent periods of acceleration. We also extend recent results on eternally accelerating open universes.
Kinnersley--type representation is constructed for the four--dimensional Einstein--Maxwell--dilaton--axion system restricted to space--times possessing two non--null commuting Killing symmetries. New representation essentially uses the matrix--valued $SL(2,R)$ formulation and effectively reduces the construction of the Geroch group to the corresponding problem for the vacuum Einstein equations. An infinite hierarchy of potentials is introduced in terms of $2\times 2$ real symmetric matrices generalizing the scalar hierarchy of Kinnersley--Chitre known for the vacuum Einstein equations.
The most general Lagrangian for non-linear electrodynamics coupled to an axion $a$ and a dilaton $ϕ$ with $SL(2,\mbox{\elevenmsb R})$ invariant equations of motion is $$ -\half\left(\nablaϕ\right)^2 - \half e^{2ϕ}\left(\nabla a\right)^2 + \fraction{1}{4}aF_{μν}\star F^{μν} + L_{\rm inv}(g_{μν},e^{-\frac{1}{2}ϕ}F_{ρσ}) $$ where $L_{\rm inv}(g_{μν},F_{ρσ})$ is a Lagrangian whose equations of motion are invariant under electric-magnetic duality rotations. In particular there is a unique generalization of Born-Infeld theory admitting $SL(2,\mbox{\elevenmsb R})$ invariant equations of motion.
We consider a very general dilaton-axion system coupled to Einstein-Hilbert gravity in arbitrary dimension and we carry out holographic renormalization for any dimension up to and including five dimensions. This is achieved by developing a new systematic algorithm for iteratively solving the radial Hamilton-Jacobi equation in a derivative expansion. The boundary term derived is valid not only for asymptotically AdS backgrounds, but also for more general asymptotics, including non-conformal branes and Improved Holographic QCD. In the second half of the paper, we apply the general result to Impr…
The symmetry structure of axion-dilaton quantum string cosmology is investigated. The invariance of the string effective action under S-duality group, SU(1,1), facilitates solution of Wheeler-De Witt equation from group theoretic considerations; revealing existence of a new class of wave functions. We discover the an underlying ${W}$-infinity algebra in this formulation.
In this paper, we investigate the influence of the angular momentum of a charged particle around non-extremal and extremal Einstein-Maxwell-Dilaton-Axion black holes on the Lyapunov exponent. The angular momentum's ranges and spatial regions where the bound of the exponent is violated are found for certain values of the rotation parameter and dilatonic constant of the black holes. This violation always exists when the rotation parameter is large enough and the rotation directions of the particle is opposite to those of the black holes. The spatial regions outside the extermal black hole for th…
Dilaton-axion modular inflation in supergravity
本文提出了四维$N=1$超引力耦合手征dilaton-axion-goldstino超多重态的新模暴涨模型，采用模不变超势和渐近模不变Kähler势，在高标度超对称破缺下实现axion稳定化，并符合宇宙微波背景辐射的精确测量。
In particle physics and cosmology, the dilaton is an hypothetical scalar field which can explain many physical phenomena. In this framework, we investigate an extended lagrangian of QCD which involves dilatonic degrees of freedom. Our approach is based on the relationship between the massive dilaton and the nonperturbative effects of QCD. We derive a general axion potential involving the dilaton properties and vacuum condensates.
Mass formulas are obtained for stationary axisymmetric solutions of the Einstein-Maxwell dilaton-axion theory, which have a regular rod structure on the axis of symmetry. Asymptotic mass, angular momentum and charge are expressed as the sums of masses, angular momenta and charges of rods dressed with field contributions. The calculation is based on a three-dimensional sigma model representation of the stationary EMDA system and the Tomimatsu approach proposed for the Einstein-Maxwell system. Our results provide an alternative interpretation of mass formulas and thermodynamics for black holes w…
We derive a set of complex potentials which linearize the action of charging symmetries of the stationary Einstein-Maxwell dilaton-axion theory.
We study the quantum cosmology of the 2D Hawking-Page massless scalar-field model and the homogeneous and isotropic dilation-axion string cosmology.For both models we find new exact solutions for the Wheeler-DeWitt equation and for the supersymmetric wave function equations. We show that the Wheeler-DeWitt equations for the Hawking-Page model and the axion-dilaton string cosmology are invariant under a one-parameter and two-parameter squeezed transformations, respectively. These results allow to find new solutions for the wave functions of these systems at the quantum cosmology level. Also, we…
We propose the unified models of cosmological inflation, spontaneous SUSY breaking, and the dark energy (de Sitter vacuum) in $N=1$ supergravity with the dilaton-axion chiral superfield $T$ in the presence of an $N=1$ vector multiplet with the alternative Fayet-Iliopoulos term. By using the Kähler potential as $K=-α\log(T+\bar{T})$ and the superpotential as a sum of a constant and a linear term, we find that viable inflation is possible for $3\leqα\leqα_{\rm max}$ where $α_{\rm max}\approx 7.235$. Observations of the amplitude of primordial scalar perturbations fix the SUSY breaking scale in o…
Campbell et al. demonstrated the existence of axion ``hair'' for Kerr black holes due to the non-trivial Lorentz Chern-Simons term and calculated it explicitly for the case of slow rotation. Here we consider the dilaton coupling to the axion field strength, consistent with low energy string theory and calculate the dilaton ``hair'' arising from this specific axion source.
We present a new solution to dilaton-axion gravity which looks like a rotating Bertotti-Robinson (BR) Universe. It is supported by an homogeneous Maxwell field and a linear axion and can be obtained as a near-horizon limit of extremal rotating dilaton-axion black holes. It has the isometry $SL(2,R)\times U(1)$ where U(1) is the remnant of the SO(3) symmetry of BR broken by rotation, while $SL(2,R)$ corresponds to the $AdS_2$ sector which no longer factors out of the full spacetime. Alternatively our solution can be obtained from the D=5 vacuum counterpart to the dyonic BR with equal electric a…
We propose the supersymmetric extension of the modified Born-Infeld-axion-dilaton non-linear electrodynamics that has confined static abelian solutions used for describing the electromagnetic confinement in the presence of axion and dilaton fields, and charged matter. The supersymmetric extension also has the non-trivial scalar potential that implies the upper bounds on the matter fields.
The ten--parametric internal symmetry group is found in the $D=4$ Einstein--Maxwell--Dilaton--Axion theory restricted to space--times admitting a Killing vector field. The group includes dilaton--axion $SL(2,R)$ duality and Harrison--type transformations which are similar to some target--space duality boosts, but act on a different set of variables. New symmetry is used to derive a seven--parametric family of rotating dilaton--axion Taub--NUT dyons.
Stationary four-dimensional BPS solutions to gravity coupled bosonic theories admitting a three-dimensional sigma-model representation on coset spaces are interpreted as null geodesics of the target manifold equipped with a certain number of harmonic maps. For asymptotically flat (or Taub-NUT) space-times such geodesics can be directly parametrized in terms of charges saturating the Bogomol'nyi-Gibbons-Hull bound, and classified according to the structure of related coset matrices. We investigate in detail the ``dilaton-axion gravity'' with one vector field, and show that in the space of BPS s…
We calculate dilaton and axion radiation generated in the collision of two straight initially unexcited strings and give a rough cosmological estimate of dilaton and axion densities produced via this mechanism in the early universe.
We show that the D=5 dilaton-axion gravity compactified on a 2-torus possesses the SL(4,R)/SO(4) matrix formulation. It is used for construction of the SO(2,2)-invariant BPS solution depended on the one harmonic function.
The discrepancy in measurements of the Hubble constant indicates new physics in dark energy, dark matter, or both. Drawing inspiration from string theory, where axions interact with the other moduli fields, including the dilaton, here we demonstrate that the dynamics of an interacting dilaton and axion naturally realizes the proposal of Early Dark Energy. In this setup, stabilization of the the dilaton is in part due to the axion, and in the early universe the dilaton contributes to dark energy. The combined axion-dilaton system is destabilized when the Hubble constant falls below the mass of …
Kink in the dilaton-axion theory with a potential possessing dilaton shift symmetry
本文推广含胀子与轴子的 sigma 模型，引入具有胀子平移对称性的势，在 (1+1) 维中构造出任意耦合常数下带非平凡胀子分布的轴子型扭结，并求得其质量。
The gauge-fixed action of a `spacetime-filling' D3-brane with dilaton-axion coupling is formulated in N=1 superspace. We investigate its symmetries by paying special attention to a possible non-linearly realized extra (hidden) supersymmetry, and emphasize the need of a linear superfield coupled to an abelian Chern-Simons superfield to represent a dilaton-axion supermultiplet in the off-shell manifestly supersymmetric approach.
The Kramer--Neugebauer--like transformation is constructed for the stationary axisymmetric D=4 Einstein--Maxwell--dilaton--axion system. This transformation directly maps the dualized sigma--model equations of the theory into the nondualized ones. Also the new chiral $4 \times 4$ matrix representation of the problem is presented.
A set of consistency conditions is derived for the massless sector of the D-dimensional E(8)xE(8) heterotic string. Under the solvable Lie algebra gauge these conditions are further formulated explicitly in terms of the dilatons and the axions. It is then shown that these consistency conditions which are satisfied by the solution space give way to an implicit decoupling between the coset scalar sector namely the dilatons and the axions and the gauge fields of the theory.
Rotation angle of the plane of polarization of the distant galactic radio waves has been estimated in a string inspired axion-dilaton background. It is found that the axion,dual to the field strength of the second rank antisymmetric massless Kalb-Ramond field in the string spectrum, produces a wavelength independent optical rotation which is much larger than that produced by the dilaton. Detection of such rotation has been reported in some recent cosmological experiments. The observed value has been compared with our estimated theoretical value following various cosmological constraints. The e…
Higgs-dilaton model revisited: can dilaton act as QCD axion?
本文重新审视 Higgs-dilaton 模型，探讨 dilaton 作为 QCD 轴子解决强 CP 问题，并证明其可在低尺度暴胀后形成暗物质，构建了与 CMB 数据兼容的 Higgs 驱动暴胀模型。
A generalization of Born-Infeld non-linear vacuum electrodynamics involving axion and dilaton fields is constructed with couplings dictated by electromagnetic duality and SL(2,R) symmetries in the weak field limit. Besides the Newtonian gravitational constant the model contains a single fundamental coupling parameter b0. In the absence of axion and dilaton interactions it reduces, in the limit as b0 tends to infinity, to Maxwell's linear vacuum theory while for finite b0 it reduces to the original Born-Infeld model. The spherically symmetric static sector of the theory is explored in a backgro…
We study the Brans-Dicke model in the presence of an axion. The dynamical equations are solved when the fields are space independent and the metric is spatially flat. It is found that at late time the scale factor undergoes decelerated expansion but the dilaton grows large. At early time, scale factor and the dilaton approach constants.
The generic scale-invariant theory of an axion and a dilaton coupled to gravity in $d$-dimensions is generalized to a `universal' one-axion model with two dilatons that reproduces itself under consistent dimensional-reduction/truncation. Flat FLRW cosmologies are shown to correspond to trajectories of a three-dimensional autonomous dynamical system, which we analyse with a focus on accelerated cosmic expansion, deriving the precise swampland bounds that exclude eternal acceleration. We also show that for two sets of values of its three independent parameters, the model is a consistent truncati…
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