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 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}.
$AdS_{5}$ 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…
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…
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…
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…
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 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…
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…
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…
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 …
Recently it was proposed that asymptotically flat spacetimes have a holographic dual which is an ultra-relativistic conformal field theory. In this paper, we obtain the conformal anomaly for such a theory via the flat-space holography technique. Furthermore, using flat-space holography we obtain a C-function for this theory which is monotonically decreasing from the UV to the IR by employing the null energy condition in the bulk.
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…
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 hi…
We advance a construction for the balanced partial entanglement entropy (BPE) for bipartite mixed states in a class of $(1+1)$-dimensional Galilean conformal field theories dual to Einstein gravity and topologically massive gravity in asymptotically flat spacetimes. We compare our results with the entanglement wedge cross section (EWCS) in the dual geometries and find exact agreement. Furthermore, utilizing a geometric picture, we demonstrate the holographic duality between the EWCS and the BPE in the context of flat holography.
We present the construction of BMS$_3$ blocks in a two-dimensional field theory and compare the results with holographic computations involving probe particles propagating in flat space cosmologies. On the field theory side, we generalize the monodromy method used in the context of AdS/CFT to theories with BMS symmetry. On the bulk side we consider geodesic Feynman diagrams, recently introduced in [arXiv:1712.07131], evaluated in locally flat geometries generated by backreaction of heavy BMS primary operators. We comment on the implications of these results for the eigenstate thermalization hy…
We prove the flat space analogue of the Flato-Fronsdal theorem. It features the flat space singleton representation suggested recently. We do that by deriving a kernel that intertwines a pair of singleton representations with massless higher-spin fields in flat space. Next, we derive two-point functions of flat space singletons, which are then used to construct two- and three-point scattering amplitudes in the dual theory of massless higher-spin fields. These amplitudes agree with amplitudes in the chiral higher-spin theory.
We obtain the reflected entropy for bipartite states in a class of $(1+1)$-dimensional Galilean conformal field theories ($GCFT_{1+1}$) through a replica technique. Furthermore we compare our results with the entanglement wedge cross section (EWCS) obtained for the dual (2+1) dimensional asymptotically flat geometries in the context of flat holography. We find that our results are consistent with the duality between the reflected entropy and the bulk EWCS for flat holographic scenarios.
We compute the leading corrections to the Bekenstein-Hawking entropy of the Flat Space Cosmological (FSC) solutions in 3D flat spacetimes, which are the flat analogues of the BTZ black holes in AdS3. The analysis is done by a computation of density of states in the dual 2D Galilean Conformal Field Theory and the answer obtained by this matches with the limiting value of the expected result for the BTZ inner horizon entropy as well as what is expected for a generic thermodynamic system. Along the way, we also develop other aspects of holography of 3D flat spacetimes.
We propose a quasi-local stress tensor for the four-dimensional asymptotically flat Robinson-Trautman geometries by taking the flat-space limit from the corresponding asymptotically AdS solutions. This stress tensor results in the correct charges of the generators of BMS symmetry if we define conformal infinity by an anisotropic scaling of the metric components. Using flat-space holography this stress tensor is related to expectation values of the stress tensor in a dual field theory called BMS-invariant field theory (BMSFT). We also calculate the two and three point functions of the proposed …
We develop models of 1+1 dimensional dilaton gravity describing flows to $AdS_2$ from higher dimensional $AdS$ and other spaces. We use these to study the effects of backreaction on holographic correlators. We show that this scales as a relevant effect at low energies, for compact transverse spaces. We also discuss effects of matter loops, as in the CGHS model.
We extend the reflected entropy to the bipartite state in a two dimensional Galilean conformal field theory ($GCFT_2$) which is dual to the asymptotically flat spacetime described by the generalized minimal massive gravity (GMMG). To this end we consider the Renyi entanglement entropy formula that can be related to the reflected entropy by some manipulations of the replica technique. In a limited case, we find the reflected entropy is twice the minimal entanglement wedge cross section (EWCS) and this is an evidence on the relation between the reflected entropy and the EWCS in the flat holograp…
We point out that aspects of quantum mechanics can be derived from the holographic principle, using only a perturbative limit of classical general relativity. In flat space, the covariant entropy bound reduces to the Bekenstein bound. The latter does not contain Newton's constant and cannot operate via gravitational backreaction. Instead, it is protected by - and in this sense, predicts - the Heisenberg uncertainty principle.
We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual $(1+1)$-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual $AdS/CFT$ …
The odd entanglement entropy (OEE) for bipartite states in a class of $(1+1)$-dimensional Galilean conformal field theories ($GCFT_{1+1}$) is obtained through an appropriate replica technique. In this context our results are compared with the entanglement wedge cross section (EWCS) for $(2+1)$-dimensional asymptotically flat geometries dual to the $GCFT_{1+1}$ in the framework of flat holography. We find that our results are consistent with the duality of the difference between the odd entanglement entropy and the entanglement entropy of bipartite states, with the bulk EWCS for flat holographi…
We find a class of asymptotically flat slowly rotating charged black hole solutions of Einstein-Maxwell-dilaton theory with arbitrary dilaton coupling constant in higher dimensions. Our solution is the correct one generalizing the four-dimensional case of Horne and Horowitz \cite{Hor1}. In the absence of a dilaton field, our solution reduces to the higher dimensional slowly rotating Kerr-Newman black hole solution. The angular momentum and the gyromagnetic ratio of these rotating dilaton black holes are computed. It is shown that the dilaton field modifies the gyromagnetic ratio of the black h…
We study the chiral flat space higher-spin algebra, which is the global symmetry algebra of the chiral higher-spin theory in the 4d Minkowski space. We find that it can be constructed as the universal enveloping algebra of a certain chiral deformation of the Poincare algebra quotiented by a set of quadratic identities. These identities allow us to identify a representation of the latter algebra, which by analogy with the AdS space higher-spin holography, we interpret as the flat space singleton representation. We provide two explicit realisations of this singleton representation -- in terms of…
We propose an explicit realization of flat space holography in two dimensions where both sides of the duality are independently defined and the boundary theory is completely solvable. In the bulk, we define a novel $\mathcal{N}=1$ flat space supergravity theory and exactly compute the full topological expansion of its Euclidean partition function with an arbitrary number of boundaries. On the boundary, we consider a double scaled Hermitian random matrix model with Gaussian potential and use the loop equations to show it independently reproduces the bulk partition function to all orders in the …
We discuss AdS$_2$ quantum gravity from an unconventional perspective that emphasizes bulk geometry. In our approach, AdS$_2$ has no boundary, there are no divergences that require renormalization, and the dilaton of JT-gravity can be omitted altogether. The result is the standard Schwarzian theory. However, it may be advantageous that our derivation just relies on conventional AdS/CFT correspondence and effective quantum field theory. For example, it clarifies the symmetry breaking pattern. It also puts the non-compact AdS$_2$ topology on the same footing as compact Riemann surfaces.
Riemannian coordinates for flat metrics corresponding to three--dimensional conformal Poisson--Lie T--dualizable sigma models are found by solving partial differential equations that follow from the transformations of the connection components. They are then used for finding general forms of the dilaton fields satisfying the vanishing beta equations of the sigma models.
BMS symmetry, which is the asymptotic symmetry at null infinity of flat spacetime, is an important input for flat holography. In this paper, we give a holographic calculation of entanglement entropy and Rényi entropy in three dimensional Einstein gravity and Topologically Massive Gravity. The geometric picture for the entanglement entropy is the length of a spacelike geodesic which is connected to the interval at null infinity by two null geodesics. The spacelike geodesic is the fixed points of replica symmetry, and the null geodesics are along the modular flow. Our strategy is to first reform…
We derive new rotating, non-asymptotically flat black ring solutions in five-dimensional Einstein-Maxwell-dilaton gravity with dilaton coupling constant $α=\sqrt{8/3}$ which arises from a six-dimensional Kaluza-Klein theory. As a limiting case we also find new rotating, non-asymptotically flat five-dimensional black holes. The solutions are analyzed and the mass, angular momentum and charge are computed. A Smarr-like relation is found. It is shown that the first law of black hole thermodynamics is satisfied.
We use the correspondence between three-dimensional asymptotically flat spacetimes and two-dimensional contracted conformal field theories (CCFTs) to derive the stress tensor correlators of CCFT$_2$. On the gravity side we use the metric formulation instead of the Chern-Simons formulation of three-dimensional gravity. This method can also be used for four-dimensional case where there is no Chern-Simons formulation for the bulk theory.
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 …
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a striking resemblance with observables in 2d BF (plus a boundary term), associated to a quantum deformation of $SL(2,\mathbb{R})$, a connection we develop in some detail. For the case of the $(2,p)$ minimal string theory, we compare and match the results from the continuum approach with a matrix model calculation, and verify that in the large $p$ limit the c…
We systematically derive the asymptotically flat five dimensional black rings in EMd gravity by using the sigma model structure of the dimensionally reduced field equations. New non-asymptotically flat EMd black ring solutions in five dimensions are also constructed and their physical properties are analyzed.
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…
Transformations between group coordinates of three--dimensional conformal sigma models in the flat background and their flat, i.e. Riemannian coordinates enable to find general dilaton fields for three-dimensional flat sigma models. By the Poisson-Lie transformation we can get dilatons for the dual sigma models in a curved background. Unfortunately, in some cases the dilatons depend on inadmissible auxiliary variables so the procedure is not universal. The cases where the procedure gives proper and nontrivial dilatons in curved backgrounds are investigated and results given.
We study several aspects of holographic entanglement in two models known as flat$_3$/BMSFT and (W)AdS$_3$/WCFT. These are two examples of holography beyond AdS/CFT where the the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS$_3$ or A…
In this paper we study non-commutative Yang-Mills theory (NCYM) through its gravity dual. First it is shown that the gravity dual of an NCYM with self-dual $θ$-parameters has a Lagrangian in the form of five-dimensional dilatonic gravity. Then we use the de-Boer-Verlinde-Verlinde formalism for holographic renormalization group flows to calculate the coefficient functions in the Weyl anomaly of the NCYM at low energies under the assumption of potential dominance, and show that the $C$-theorem holds true in the present case.
We provide a first derivation of the Bekenstein-Hawking entropy of 3d flat cosmological horizons in terms of the counting of states in a dual field theory. These horizons appear in the shifted-boost orbifold of R^{1,2}, the flat limit of non-extremal rotating BTZ black holes. These 3d geometries carry non-zero charges under the asymptotic symmetry algebra of R^{1,2}, the 3d Bondi-Metzner-Sachs (BMS3) algebra. The dual theory has the symmetries of the 2d Galilean Conformal Algebra, a contraction of two copies of the Virasoro algebra, which is isomorphic to BMS3. We study flat holography as a li…
Recently, Klemm and others [hep-th/0104141] have successfully generalized the Cardy-Verlinde formula for an asymptotically flat spacetime of arbitrary dimensionality. And yet, from a holographic perspective, the interpretation of this formula remains somewhat unclear. Nevertheless, in this paper, we incorporate the implied flat space/CFT duality into a study on boundary descriptions of a $d$-dimensional Schwarzschild-black hole spacetime. In particular, we demonstrate that the (presumably) dual CFT adopts a string-like description and, moreover, is thermodynamically equivalent to a string that…
We propose a stress tensor for the Kerr black hole written in the Boyer-Lindquist coordinate. To achieve this, we use the dictionary of the Flat/CCFT correspondence and take the flat-space limit from the quasi-local stress tensor of the four-dimensional Kerr-AdS black hole. The proposed stress tensor yields the correct values for the mass and angular momentum of the Kerr black hole at spatial infinity. We also calculate some components of the energy momentum tensor of the three dimensional CCFT and show that they are consistent with the holographic calculation of the Kerr black hole. The calcu…
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…
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 study the islands and the Page curve in the 1+1-dimensional eternal dilaton black hole models. Without islands, the entanglement entropy of the radiation grows linearly at late time. However with an island, its growth stops at the value of almost twice of the black hole entropy. Therefore an island emerges at the late time, and the entanglement entropy of the radiation shows the Page curve.
