The AdS/CFT correspondence in two dimensions

We review recent progress in understanding the anti-de Sitter/conformal field theory correspondence in the context of two-dimensional dilaton gravity theory.Comment: Contribution to the Proceedings of the Euroconference on "Brane New World and Noncommutative Geometry", Turin, October 200

2D Extremal Black Holes as Solitons

We discuss the relationship between two-dimensional (2D) dilaton gravity models and sine-Gordon-like field theories. We show that there is a one-to-one correspondence between the solutions of 2D dilaton gravity and the solutions of a (two fields) generalization of the sine-Gordon model. In particular, we find a connection between the soliton solutions of the generalized sine-Gordon model and extremal black hole solutions of 2D dilaton gravity. As a by-product of our calculations we find a easy way to generate cosmological solutions of 2D dilaton gravity.Comment: 12 pages, LaTex, no figures, typos correcte

Multi-black holes and instantons in effective string theory

The effective action for string theory which takes into account non-minimal coupling of moduli admits multi-black hole solutions. The euclidean continuation of these solutions can be interpreted as an instanton mediating the splitting and recombination of the throat of extremal magnetically charged black holes.Comment: 10 pages, plain Te

Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity

We investigate static, planar, solutions of Einstein-scalar gravity admitting an anti-de Sitter (AdS) vacuum. When the squared mass of the scalar field is positive and the scalar potential can be derived from a superpotential, minimum energy theorems indicate the existence of a scalar soliton. On the other hand, for these models, no-hair theorems forbid the existence of hairy black brane solutions with AdS asymptotics. By considering a specific example (an exact integrable model which has the form of a Toda molecule) and by deriving explicit exact solution, we show that these models allow for hairy black brane solutions with non-AdS domain wall asymptotics, whose extremal limit is a scalar soliton. The soliton smoothly interpolates between a non-AdS domain wall solution at $r=\infty$ and an AdS solution near $r=0$.Comment: 5 pages, no figure

Phase transition and hyperscaling violation for scalar Black Branes

We investigate the thermodynamical behavior and the scaling symmetries of the scalar dressed black brane (BB) solutions of a recently proposed, exactly integrable Einstein-scalar gravity model [1], which also arises as compactification of (p-1)-branes with a smeared charge. The extremal, zero temperature, solution is a scalar soliton interpolating between a conformal invariant AdS vacuum in the near-horizon region and a scale covariant metric (generating hyperscaling violation on the boundary field theory) asymptotically. We show explicitly that for the boundary field theory this implies the emergence of an UV length scale (related to the size of the brane), which decouples in the IR, where conformal invariance is restored. We also show that at high temperatures the system undergoes a phase transition. Whereas at small temperature the Schwarzschild-AdS BB is stable, above a critical temperature the scale covariant, scalar-dressed BB solution, becomes energetically preferred. We calculate the critical exponent z and the hyperscaling violation parameter of the scalar-dressed phase. In particular we show that the hyperscaling violation parameter is always negative. We also show that the above features are not a peculiarity of the exact integrable model of Ref.[1], but are a quite generic feature of Einstein-scalar and Einstein-Maxwell-scalar gravity models for which the squared-mass of the scalar field is positive and the potential vanishes exponentially as the scalar field goes to minus infinity.Comment: 20 pages, 4 figures. In the revised version it has been pointed out that the Einstein-scalar gravity model considered in the paper also arises as compactification of black p-branes with smeared charge

Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field

We propose a general method for solving exactly the static field equations of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. Our method starts from an ansatz for the scalar field profile, and determines, together with the metric functions, the corresponding form of the scalar self-interaction potential. Using this method we prove a new no-hair theorem about the existence of hairy black-hole and black-brane solutions and derive broad classes of static solutions with radial symmetry of the theory, which may play an important role in applications of the AdS/CFT correspondence to condensed matter and strongly coupled QFTs. These solutions include: 1) four- or generic $(d+2)$-dimensional solutions with planar, spherical or hyperbolic horizon topology; 2) solutions with AdS, domain wall and Lifshitz asymptotics; 3) solutions interpolating between an AdS spacetime in the asymptotic region and a domain wall or conformal Lifshitz spacetime in the near-horizon region.Comment: Some references adde

Sine-Gordon solitons, auxiliary fields, and singular limit of a double pendulums chain

We consider the continuum version of an elastic chain supporting topological and non-topological degrees of freedom; this generalizes a model for the dynamics of DNA recently proposed and investigated by ourselves. In a certain limit, the non-topological degrees of freedom are frozen, and the model reduces to the sine-Gordon equations and thus supports well-known topological soliton solutions. We consider a (singular) perturbative expansion around this limit and study in particular how the non-topological field assume the role of an auxiliary field. This provides a more general framework for the slaving of this degree of freedom on the topological one, already observed elsewhere in the context of the mentioned DNA model; in this framework one expects such phenomenon to arise in a quite large class of field-theoretical models.Comment: 18 pages, 2 figure

Acoustic horizons for axially and spherically symmetric fluid flow

We investigate the formation of acoustic horizons for an inviscid fluid moving in a pipe in the case of stationary and axi-symmetric flow. We show that, differently from what is generally believed, the acoustic horizon forms in correspondence of either a local minimum or maximum of the flux tube cross-section. Similarly, the external potential is required to have either a maximum or a minimum at the horizon, so that the external force has to vanish there. Choosing a power-law equation of state for the fluid, $P\propto \rho^{n}$, we solve the equations of the fluid dynamics and show that the two possibilities are realized respectively for $n>-1$ and $n<-1$. These results are extended also to the case of spherically symmetric flow.Comment: 6 pages, 3 figure

Entropy bounds in two dimensions

We discuss entropy bounds for a class of two-dimensional gravity models. While the Bekenstein bound can be proved to hold in general for weakly gravitating matter, the analogous of the holographic bound is not universal, but depends on the specific model consideredComment: 5 pages, plain Te

Double-bounce domain-wall in Einstein-Yang-Mills-Scalar black holes

We find Einstein-Yang-Mills (EYM) black hole solutions endowed with massless scalar hair in the presence of a potential $V\left(\phi \right)$ as function of the scalar field $\phi$. Choosing $V\left(\phi \right) =$constant (or zero) sets the scalar field to vanish leaving us with the EYM black holes. Our class of black hole solutions is new so that they do not asymptote in general to any known limits. Particular case is given, however, which admits an asymptotically anti de Sitter limit in $6-$dimensional spacetime. The role of the potential $V\left(\phi \right)$ in making double bounces (i.e. both a minimum and maximum radii) on a Domain Wall (DW) universe is highlighted.Comment: 9 pages, 1 figure, final version for publication in EPJ