The asymptotically-logarithmically-AdS black-hole solutions of 5D dilaton gravity with a monotonic dilaton potential are analyzed in detail. Such theories are holographically very close to pure Yang-Mills theory in four dimensions. The existence and uniqueness of black-hole solutions is shown. It is also shown that a Hawking-Page transition exists at finite temperature if and only if the potential corresponds to a confining theory. The physics of the transition matches in detail with that of deconfinement of the Yang-Mills theory. The high-temperature phase asymptotes to a free gluon gas at high temperature matching the expected behavior from asymptotic freedom. The thermal gluon condensate is calculated and shown to be crucial for the existence of a non-trivial deconfining transition. The condensate of the topological charge is shown to vanish in the deconfined phase.
We study several aspects of charged dilaton black holes with planar symmetry in $(d+2)$-dimensional spacetime, generalizing the four-dimensional results investigated in arXiv:0911.3586 [hep-th]. We revisit the exact solutions with both zero and finite temperature and discuss the thermodynamics of the near-extremal black holes. We calculate the AC conductivity in the zero-temperature background by solving the corresponding Schrödinger equation and find that the AC conductivity behaves like $ω^δ$, where the exponent $δ$ is determined by the dilaton coupling $α$ and the spacetime dimension parame…
In this proceedings contribution we summarize and discuss results of Refs. \cite{Grumiller:2013swa, Grumiller:2015vaa} in the light of recent developments in $\textrm{AdS}_2$ holography \cite{Maldacena:2016upp, Jensen:2016pah, Engelsoy:2016xyb}.
We study the holographic non-relativistic fermions in the presence of bulk dipole coupling in charged dilatonic black hole background. We explore the nontrivial effects of the bulk dipole coupling, the fermion charge as well as the dilaton field on the flat band, the Fermi surface and the emergence of the gap by investigating the spectral function of the non-relativistic fermion system. In particular, we find that the presence of the flat band in the non-relativistic case will suppress the Fermi momentum. Besides, we observe that the effect of the dipole coupling in the dilaton gravity is more…
We study generic two-dimensional dilaton gravity with a Maxwell field and prove its triviality for constant dilaton boundary conditions, despite of the appearance of a Virasoro algebra with non-zero central charge. We do this by calculating the canonical boundary charges, which turn out to be trivial, and by calculating the quantum gravity partition function, which turns out to be unity. We show that none of the following modifications changes our conclusions: looser boundary conditions, non-linear interactions of the Maxwell field with the dilaton, inclusion of higher spin fields, inclusion o…
$AdS_{5}$ with linear dilaton and non vanishing $B$-field is shown to be a solution of the non critical string beta function equations. A non critical $(D=5)$ solution interpolating between flat space-time and $AdS_{5}$, with asymptotic linear dilaton and non vanishing $B$-field is also presented. This solution is free of space-time singularities and has got the string coupling constant everywhere bounded. Both solutions admit holographic interpretation in terms of ${\cal N}=0$ field theories. Closed string tachyon stability is also discussed.
We consider the first subleading terms in the low-energy cross section for the absorption of dilaton partial waves by D3-branes. We demonstrate that these corrections, computed previously via supergravity, can be reproduced exactly in a worldvolume calculation using a deformation of N=4 SYM theory by a dimension eight chiral operator. The calculation does not depend on how the theory is regularized. This result provides another hint that holographic duality between the D3-brane worldvolume theory and the corresponding supergravity solution may be valid beyond the near horizon limit.
Asymptotic AdS Riemann space-times in five dimensions with a black brane (horizon) sourced by a fully back-reacted scalar field (dilaton) offer -- via the holographic dictionary -- various options for the thermodynamics of the flat four-dimensional boundary theory, uncovering Hawking-Page, first-order and second-order phase transitions up to a cross-over or featureless behavior. The relation of these phase structures to the dilaton potential is clarified and illustrating examples are presented. Having in mind applications to QCD we study probe vector mesons with the goal to figure out conditio…
We present a revisitation of the Almheiri-Polchinski dilaton gravity model from a two-dimensional (2D) bulk perspective. We describe a peculiar feature of the model, namely the pattern of conformal symmetry breaking using bulk Killing vectors, a covariant definition of mass and the flow between different vacua of the theory. We show that the effect of the symmetry breaking is both the generation of an infrared scale (a mass gap) and to make local the Goldstone modes associated with the asymptotic symmetries of the 2D spacetime. In this way a non vanishing central charge is generated in the dua…
We investigate bulk and holographic features of finite-temperature black brane solutions of 4D anti-de Sitter Einstein-Maxwell-dilaton-gravity (EMDG). We construct, numerically, black branes endowed with non trivial scalar hairs for broad classes of EMDG. We consider both exponential and power-law forms for the coupling functions, as well as several charge configurations: purely electric, purely magnetic and dyonic solutions. At finite temperature the field theory holographically dual to these black brane solutions has a rich and interesting phenomenology reminiscent of electron motion in meta…
We present an interacting spin-2 gauge theory coupled to the two-dimensional dilaton-gravity in flat spacetime. The asymptotic symmetry group is enhanced to the central extension of Diff$(S^1)\ltimes C^\infty(S^1)\ltimes$Vec($S^1$) when the central element of the Heisenberg subgroup is zero (vanishing $U(1)$ level). Using the BF-formulation of the model we derive the corresponding boundary coadjoint action which is the spin-2 extension of the warped Schwarzian theory at vanishing $U(1)$ level. We also discuss the thermodynamics of black holes in this model.
In the background of a charged AdS dilaton black hole, we investigate the movement of a self-graviting 3-brane and relevant holographic effects as the brane move close to the AdS boundary. The induced metric on brane corresponds to an exact FLRW geometry, while the evolution of brane is determined by Israel junction condition and the effective Einstein field equation on brane together. When the brane approaches the AdS boundary, AdS/CFT correspondence implies that a radiation dominated FLRW-universe ($P=\frac{1}{3}ρ$) should be given. According to the holographic renormalization procedure, we …
We discuss aspects of generic 2-dimensional dilaton gravity theories. The 2-dim geometry is in general conformal to $AdS_2$ and has IR curvature singularities at zero temperature: this can be regulated by a black hole. The on-shell action is divergent: we discuss the holographic energy-momentum tensor by adding appropriate counterterms. For theories obtained by dimensional reduction of the gravitational sector of higher dimensional theories, for instance higher dimensional $AdS$ gravity as a concrete example, the 2-dimensional description dovetails with the higher dimensional one. We also disc…
We argue that vacua of string theory which asymptote at weak coupling to linear dilaton backgrounds are holographic. The full string theory in such vacua is ``dual'' to a theory without gravity in fewer dimensions. The dual theory is generically not a local quantum field theory. Excitations of the string vacuum, which can be studied in the weak coupling region using worldsheet methods, give rise to observables in the dual theory. An interesting example is string theory in the near-horizon background of parallel NS5-branes, the CHS model, which is dual to the decoupled NS5-brane theory (``littl…
We study charged dilaton black branes in $AdS_4$. Our system involves a dilaton $ϕ$ coupled to a Maxwell field $F_{μν}$ with dilaton-dependent gauge coupling, ${1\over g^2} = f^2(ϕ)$. First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical techniques. The near horizon geometries in the simplest cases, where $f(ϕ) = e^{αϕ}$, are Lifshitz-like, with a dynamical exponent $z$ determined by $α$. The black hole thermodynamics varies in an interesting way with $α$, but in all cases the entropy is vanishing and the specific heat is positive …
Having in mind extensions of 2D holography beyond the Jackiw-Teitelboim model we propose holographic counterterms and asymptotic conditions for a family of asymptotically AdS$_2$ dilaton gravity models leading to a consistent variational problem and a finite on-shell action. We show the presence of asymptotic Virasoro symmetries in all these models. The Schwarzian action generates (a part) of the equations of motion governing the asymptotic degrees of freedom. We also analyse the applicability of various entropy formulae. By a dilaton-dependent conformal transformation our results are extended…
Exact conditions on the clock parameters corresponding to the minimal uncertainty in distance measurement are derived in uniform manner for any number of space time dimensions. The result espouses the holography principle no matter what the number of space time dimensions is. In this context the ADD braneworld model is considered. Some remarks are made on deviation of holography as well as of special relativity at the scales provided by the cosmological constant. We also comment on the potential influence of the background radiation on the uncertainty in length measurement. The presence of una…
We investigate consistent charged black hole solutions to the Einstein-Maxwell-Dilaton (EMD) equations that are asymptotically AdS. The solutions are gravity duals to phases of a non-conformal plasma at finite temperature and density. For the dilaton we take a quadratic ansatz leading to linear confinement at zero temperature and density. We consider a grand canonical ensemble, where the chemical potential is fixed, and find a rich phase diagram involving the competition of small and large black holes. The phase diagram contains a critical line and a critical point similar to the van der Waals…
We study various transitions in dilaton holography, including those associated with the spontaneous breaking of a global (superfluid case) or local (superconductor case) U(1) symmetry in diverse dimensions d. By analyzing the thermodynamics of the dilaton-gravity system we find that scale invariance is broken at low temperatures, as shown by a nontrivial hyperscaling violation exponent in the infrared; increasing the temperature we recover scale symmetry in a d dependent way: while for d=2+1 a phase transition is found, for d=3+1 the transition is rather a crossover. This is the expected behav…
Taking a thermodynamic perspective, we study the weak gravity conjecture in the context of 4D Einstein-Maxwell-dilaton theory. We find closed-form expressions for the corrected thermodynamic quantities in the presence of four-derivative terms in the action, and in particular the charge-to-mass ratio and entropy, for several families of solutions of special magnetic-to-electric charge ratio or dilaton coupling constant. Assuming that dyonic black holes themselves are the conjectured charged states, this places constraints on the Wilson coefficients of the theory which we show are satisfied unde…
We consider a system consisting of $5$ dimensional gravity with a negative cosmological constant coupled to a massless scalar, the dilaton. We construct a black brane solution which arises when the dilaton satisfies linearly varying boundary conditions in the asymptotically $AdS_5$ region. The geometry of this black brane breaks rotational symmetry while preserving translational invariance and corresponds to an anisotropic phase of the system. Close to extremality, where the anisotropy is big compared to the temperature, some components of the viscosity tensor become parametrically small compa…
We study black branes carrying both electric and magnetic charges in Einstein-Maxwell theory coupled to a dilaton-axion in asymptotically anti de Sitter space. After reviewing and extending earlier results for the case of electrically charged branes, we characterise the thermodynamics of magnetically charged branes. We then focus on dyonic branes in theories which enjoy an $SL(2,R)$ electric-magnetic duality. Using $SL(2,R)$, we are able to generate solutions with arbitrary charges starting with the electrically charged solution, and also calculate transport coefficients. These solutions all e…
We study the graviton phenomenology of TeV Little String Theory by exploiting its holographic gravity dual five-dimensional theory. This dual corresponds to a linear dilaton background with a large bulk that constrains the Standard Model fields on the boundary of space. The linear dilaton geometry produces a unique Kaluza-Klein graviton spectrum that exhibits a ~ TeV mass gap followed by a near continuum of narrow resonances that are separated from each other by only ~ 30 GeV. Resonant production of these particles at the LHC is the signature of this framework that distinguishes it from large …
We systematically investigate the sound modes of momentum dissipated holographic systems. In particular, we focus on the Einstein-linear axions and the Einstein-Maxwell-dilaton-axion theories in four-dimensional bulk spacetime dimensions. The sound velocities of the two theories are computed respectively and the sound attenuation of the Einstein-Maxwell-axion theory is also calculated analytically. We also obtain numeral dispersion relations in the two theories which match with our analytical results. Our results show that the sound velocity of the Einstein-Maxwell-dilaton theory with addition…
AdS black holes in two-dimensional dilaton gravity and holography
Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学）；Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学物理与数学科学学院）；Instituto de Física, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学物理研究所）
Holographic models for the pure gauge QCD vacuum are explored. The holographic renormalization of these models is considered as required by a phenomenological approach that takes the $β$-functions of the models as the only input. This approach is done taking the dilaton as the coordinate orthogonal to the border. This choice greatly simplifies the analysis and gives a geometrical interpretation for the fixed points of the renormalization group flow. Examples are constructed that present asymptotic freedom, confinement of static quarks, either with vanishing or non-vanishing gluon condensate $G…
We relate various black hole solutions in the near-horizon region to black hole solutions in two-dimensional dilaton gravity theories in order to argue that thermodynamics of black holes in D>=4 can be effectively described by thermodynamics of black holes in two-dimensional dilaton gravity theories. We show that the Bekenstein-Hawking entropies of single-charged dilatonic black holes and dilatonic p-branes with an arbitrary dilaton coupling parameter in arbitrary spacetime dimensions are exactly reproduced by the Bekenstein-Hawking entropy of the two-dimensional black hole in the associated t…
Gauge theories living on stacks of D7-branes are holographically related to IIB gravitational backgrounds with a varying axion-dilaton field (F-theory). The axion-dilaton field is generated by D7, O7 and D-instanton sources and can be written in terms of the chiral correlators of the eight dimensional gauge theory living on the D7-branes. Using localization techniques, we prove that the same correlators determine the gauge coupling of the four-dimensional N=2 supersymmetric SU(2) gauge theories living on the elementary D3-brane which probes the F-theory geometries.
We show that a class of Einstein-Maxwell-Dilaton (EMD) theories are related to higher dimensional AdS-Maxwell gravity via a dimensional reduction over compact Einstein spaces combined with continuation in the dimension of the compact space to non-integral values (`generalized dimensional reduction'). This relates (fairly complicated) black hole solutions of EMD theories to simple black hole/brane solutions of AdS-Maxwell gravity and explains their properties. The generalized dimensional reduction is used to infer the holographic dictionary and the hydrodynamic behavior for this class of theori…
We study thermodynamics of (1+1) dimensional dilatonic black holes in global embedding Minkowski space scheme. Exploiting geometrical entropy correction we construct consistent entropy for the charged dilatonic black hole. Moreover, (1+1) dilatonic black holes with higher order terms are shown to possess (3+2) global flat embedding structures regardless of the details of the lapse function, and to yield a generic entropy.
All thermodynamic quantities of the Reissner-Nordström (RN) black hole can be obtained from the dilaton and its potential of two dimensional (2D) dilaton gravity. The dual relations of four thermodynamic laws are also established. Furthermore, the near-horizon thermodynamics of the extremal RN black hole is completely described by the Jackiw-Teitelboim theory which is obtained by perturbing around the AdS$_2$-horizon.
In this talk we present the latest results from our ongoing project on geometro-thermodynamics (also known as information geometry of thermodynamics or Ruppeiner geometry) of dilaton BHs in 4D in both Einstein and string frames and a dyonic dilaton BH and at the end we report very briefly results from this approach to the 2D dilaton BHs.
A large AdS Schwarzschild black hole can be approximated by an AdS planar black hole. However, the temperature of a planar black hole is not well defined due to the translational invariance of the horizon. We propose to fix this arbitrariness by imposing the entropy area law. Furthermore, using the AdS/CFT holography, we propose a relationship between the temperatures of an AdS planar and large AdS Schwarzschild black holes.
We numerically reanalyze static and spherically symmetric black hole solutions in an Einstein-Maxwell-dilaton system with a dilaton potential $m_{d}^{2}ϕ^{2}$. We investigate thermodynamic properties for various dilaton coupling constants and find that thermodynamic properties change at a critical dilaton mass $m_{d,crit}$. For $m_{d}\geq m_{d,crit}$, the black hole becomes an extreme solution for a nonzero horizon radius $r_{h,ex}$ as the Reissner-Nordström black hole. However, if $m_{d}$ is nearly equal to $m_{d,crit}$, there appears a solution of smaller horizon radius than $r_{h,ex}$. For …
New charged solutions describing black holes with squashed horizons in 5D dilaton gravity are presented. The black hole spacetimes are asymptotically locally flat and have a spacial infinity $R\times S^1\hookrightarrow S^2$. The solutions are analyzed and their thermodynamics is discussed by using the counterterm method.
Extremal black branes upon compactification in the near horizon throat region are known to give rise to $AdS_2$ dilaton-gravity-matter theories. Away from the throat region, the background has nontrivial profile. We interpret this as holographic renormalization group flow in the 2-dim dilaton-gravity-matter theories arising from dimensional reduction of the higher dimensional theories here. The null energy conditions allow us to formulate a holographic c-function in terms of the 2-dim dilaton for which we argue a c-theorem subject to appropriate boundary conditions which amount to restrictions…
In the present paper we study the long-standing problem for the thermodynamics of magnetized dilaton black holes. For this purpose we construct an exact solution describing a rotating charged dilaton black hole immersed in an external magnetic field and discuss its basic properties. We derive a Smarr-like relation and the thermodynamics first law for these magnetized black holes. The novelty in the thermodynamics of the magnetized black holes is the appearance of new terms proportional to the magnetic momentum of the black holes in the Smarr-like relation and the first law.
We study the properties of gravitational system in finite regions bounded by gravitational screens. We present the detail construction of the total energy of such regions and of the energy and momentum balance equations due to the flow of matter and gravitational radiation through the screen. We establish that the gravitational screen possesses analogs of surface tension, internal energy and viscous stress tensor, while the conservations are analogs of non-equilibrium balance equations for a viscous system. This gives a precise correspondence between gravity in finite regions and non-equilibri…
We present a formalism for studying the thermodynamics of black holes in dilaton gravity. The thermodynamic variables are defined on a quasilocal surface surrounding the black hole system and are obtained from a general class of Lagrangians involving a dilaton. The formalism thus accommodates a large number of possible theories and black hole spacetimes. Many of the thermodynamic quantities are identified from the contribution of the action on the quasilocal boundary. The entropy is found using path integral techniques, and a first law of thermodynamics is obtained. As an illustration, we calc…
We derive the first law of black rings thermodynamics in n-dimensional Einstein dilaton gravity with additional (p+1)-form field strength being the simplest generalization of five-dimensional theory containing a stationary black ring solution with dipole charge. It was done by means of choosing any cross section of the event horizon to the future of the bifurcation surface.
A new formalism for thermodynamics of AdS black holes called the {\em restricted phase space thermodynamics} (RPST) is proposed. The construction is based on top of Visser's holographic thermodynamics, but with the AdS radius fixed as a constant. Thus the RPST is free of the $(P,V)$ variables but inherits the central charge and chemical potential as a new pair of conjugate thermodynamic variables. In this formalism, the Euler relation and the Gibbs-Duhem equation hold simultaneously with the first law of black hole thermodynamics, which guarantee the appropriate homogeneous behaviors for the b…
A holographic model of probe quarkonia is presented, where the dynamical gravity-dilaton background is adjusted to the thermodynamics of 2 +1 flavor QCD with physical quark masses. The quarkonia action is modified to account for a systematic study of the heavy-quark mass dependence. We focus on the $J/ψ$ and $Υ$ spectral functions and relate our model to heavy quarkonia formation as a special aspect of hadron phenomenology in heavy-ion collisions at LHC.
We show how D-instanton corrections modify the dilaton-axion profile emitted by an O7/D7 system turning it into the non-singular F-theory background which corresponds to the effective coupling on a D3 probe.
We study non perturbative superpotentials for N=1 super Yang Mills from the point of view of large $N$ dualities. Starting with open topological strings we work out the relation between the closed string sector dilaton tadpole, which appears in the annulus amplitude, and NSNS fluxes in the closed string dual on the resolved conifold. For the mirror closed string dual version on the deformed conifold we derive, for a non vanishing $G_{3}$ form, the $N$ supersymmetric vacua and the transformations of $G_{3}$ through domain walls. Finally, as an extension of Fischler Susskind mechanism we find a …
We consider a class of domain-wall black hole solutions in the dilaton gravity with a Liouville-type dilaton potential. Using the surface counterterm approach we calculate the stress-energy tensor of quantum field theory (QFT) corresponding to the domain-wall black hole in the domain-wall/QFT correspondence. A brane universe is investigated in the domain-wall black hole background. When the tension term of the brane is equal to the surface counterterm, we find that the equation of motion of the brane can be mapped to the standard form of FRW equations, but with a varying gravitational constant…
We present a detailed analysis of the thermodynamics of exact asymptotically flat hairy black holes in Einstein-Maxwell-dilaton theory. We compute the regularized action, quasilocal stress tensor, and conserved charges by using a `counterterm method' similar to the one extensively used in the AdS-CFT duality. In the presence of a non-trivial dilaton potential that vanishes at the boundary we prove that, for some range of parameters, there exist thermodynamically stable black holes in the grand canonical and canonical ensembles. To the best of our knowledge, this is the first example of a therm…
A static spherically symmetric solution is obtained and examined in the framework of Einstein-power-Yang-Mills-dilaton theory. To derive this exact solution a dilaton potential $V(Φ)$ is taken into account. Thermodynamics of the black hole is also studied, namely we have obtained and investigated the temperature and heat capacity of the black hole which has allowed us characterize the stability of the black hole. Using the framework of the extended thermodynamic phase space we have derived the equation of state for the black hole. We have studied the Gibbs free energy of the black hole, which …
A static black hole with spherical symmetry is obtained and examined in the framework of Einstein-Yang-Mills-dilaton theory. The obtained black hole solution allowed us to derive and investigate entropy, temperature and heat capacity. To better examine the thermodynamics of the black hole extended phase space is also used. On this ground the equation of state is obtained and studied. We have also investigated the Gibbs free energy and it is shown that below the critical temperature the system demonstrates phase transitions of the first as well as of the zeroth order which is notable feature fo…
In this work, we examine how charge is transported in a theory where momentum is relaxed by spatially dependent, massless scalars. We analyze the possible IR phases in terms of various scaling exponents and the (ir)relevance of operators in the IR effective holographic theory with a dilaton. We compute the (finite) resistivity and encounter broad families of (in)coherent metals and insulators, characterized by universal scaling behaviour. The optical conductivity at zero temperature and low frequencies exhibits power tails which can violate scaling symmetries, due to the running of the dilaton…
