Holographic Description of AdS Cosmologies

To gain insight in the quantum nature of the big bang, we study the dual field theory description of asymptotically anti-de Sitter solutions of supergravity that have cosmological singularities. The dual theories do not appear to have a stable ground state. One regularization of the theory causes the cosmological singularities in the bulk to turn into giant black holes with scalar hair. We interpret these hairy black holes in the dual field theory and use them to compute a finite temperature effective potential. In our study of the field theory evolution, we find no evidence for a "bounce" from a big crunch to a big bang. Instead, it appears that the big bang is a rare fluctuation from a generic equilibrium quantum gravity state.Comment: 34 pages, 8 figures, v2: minor changes, references adde

Long Range Order at Low Temperature in Dipolar Spin Ice

Recently it has been suggested that long range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$. We report here numerical results on the low temperature properties of the dipolar spin ice model, obtained via a new loop algorithm which greatly improves the dynamics at low temperature. We recover the previously reported missing entropy in this model, and find a first order transition to a long range ordered phase with zero total magnetization at very low temperature. We discuss the relevance of these results to ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$.Comment: New version of the manuscript. Now contains 3 POSTSCRIPT figures as opposed to 2 figures. Manuscript contains a more detailed discussion of the (i) nature of long-range ordered ground state, (ii) finite-size scaling results of the 1st order transition into the ground state. Order of authors has been changed. Resubmitted to Physical Review Letters Contact: [email protected]

Asymptotically Anti-de Sitter spacetimes and scalar fields with a logarithmic branch

We consider a self-interacting scalar field whose mass saturates the Breitenlohner-Freedman bound, minimally coupled to Einstein gravity with a negative cosmological constant in D \geq 3 dimensions. It is shown that the asymptotic behavior of the metric has a slower fall-off than that of pure gravity with a localized distribution of matter, due to the back-reaction of the scalar field, which has a logarithmic branch decreasing as r^{-(D-1)/2} ln r for large radius r. We find the asymptotic conditions on the fields which are invariant under the same symmetry group as pure gravity with negative cosmological constant (conformal group in D-1 dimensions). The generators of the asymptotic symmetries are finite even when the logarithmic branch is considered but acquire, however, a contribution from the scalar field.Comment: 7 pages, CECS style, references adde

A note on spherically symmetric naked singularities in general dimension

We discuss generalizations of the recent theorem by Dafermos (hep-th/0403033) forbidding a certain class of naked singularities in the spherical collapse of a scalar field. Employing techniques similar to the ones Dafermos used, we consider extending the theorem (1) to higher dimensions, (2) by including more general matter represented by a stress-energy tensor satisfying certain assumptions, and (3) by replacing the spherical geometry by a toroidal or higher genus (locally hyperbolic) one. We show that the extension to higher dimensions and a more general topology is straightforward; on the other hand, replacing the scalar field by a more general matter content forces us to shrink the class of naked singularities we are able to exclude. We then show that the most common matter theories (scalar field interacting with a non-abelian gauge field and a perfect fluid satisfying certain conditions) obey the assumptions of our weaker theorem, and we end by commenting on the applicability of our results to the five-dimensional AdS scenarii considered recently in the literature.Comment: 16 pages, no figures, typos fixe

Nonabelian solutions in N=4, D=5 gauged supergravity

We consider static, nonabelian solutions in N=4, D=5 Romans' gauged supergravity model. Numerical arguments are presented for the existence of asymptotically anti-de Sitter configurations in the $N=4^+$ version of the theory, with a dilaton potential presenting a stationary point. Considering the version of the theory with a Liouville dilaton potential, we look for configurations with unusual topology. A new exact solution is presented, and a counterterm method is proposed to compute the mass and action.Comment: 15 pages, 4 figure

New hairy black hole solutions with a dilaton potential

We consider black hole solutions with a dilaton field possessing a nontrivial potential approaching a constant negative value at infinity. The asymptotic behaviour of the dilaton field is assumed to be slower than that of a localized distribution of matter. A nonabelian SU(2) gauge field is also included in the total action. The mass of the solutions admitting a power series expansion in $1/r$ at infinity and preserving the asymptotic anti-de Sitter geometry is computed by using a counterterm subtraction method. Numerical arguments are presented for the existence of hairy black hole solutions for a dilaton potential of the form $V(\phi)=C_1 \exp(2\alpha_1 \phi)+C_2 \exp(2\alpha_2 \phi)+C_3$, special attention being paid to the case of ${\cal N}=4, D=4$ gauged supergravity model of Gates and Zwiebach.Comment: 12 pages, 4 figures; v2:references added, typos corrected, small changes in Section

Comment on ``BCS to Bose-Einstein crossover phase diagram at zero temperature for a d_{x^2-y^2} order parameter superconductor: Dependence on the tight-binding structure''

The work by Soares et al. [Phys. Rev. B 65, 174506 (2002)] investigates the BCS-BE crossover for d-wave pairing in the 2-dimensional attractive Hubbard model. Contrary to their claims, we found that a non-pairing region does not exist in the density vs coupling phase diagram. The gap parameter at T=0, as obtained by solving analytically as well as numerically the BCS equations, is in fact finite for any non-zero density and coupling, even in the weak-coupling regime.Comment: 7 pages, 1 figur

Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity

The theory of massive gravity in three dimensions recently proposed by Bergshoeff, Hohm and Townsend (BHT) is considered. At the special case when the theory admits a unique maximally symmetric solution, a conformally flat space that contains black holes and gravitational solitons for any value of the cosmological constant is found. For negative cosmological constant, the black hole is characterized in terms of the mass and the "gravitational hair" parameter, providing a lower bound for the mass. For negative mass parameter, the black hole acquires an inner horizon, and the entropy vanishes at the extremal case. Gravitational solitons and kinks, being regular everywhere, are obtained from a double Wick rotation of the black hole. A wormhole solution in vacuum that interpolates between two static universes of negative spatial curvature is obtained as a limiting case of the gravitational soliton with a suitable identification. The black hole and the gravitational soliton fit within a set of relaxed asymptotically AdS conditions as compared with the ones of Brown and Henneaux. In the case of positive cosmological constant the black hole possesses an event and a cosmological horizon, whose mass is bounded from above. Remarkably, the temperatures of the event and the cosmological horizons coincide, and at the extremal case one obtains the analogue of the Nariai solution, $dS_{2}\times S^{1}$. A gravitational soliton is also obtained through a double Wick rotation of the black hole. The Euclidean continuation of these solutions describes instantons with vanishing Euclidean action. For vanishing cosmological constant the black hole and the gravitational soliton are asymptotically locally flat spacetimes. The rotating solutions can be obtained by boosting the previous ones in the $t-\phi$ plane.Comment: Talk given at the "Workshop on Gravity in Three Dimensions," 14-24 April 2009, ESI, Vienna. 30 pages, 6 figures. V2: minor changes and section 6 slightly improved. Last version for JHE

Multitrace deformations, Gamow states, and Stability of AdS/CFT

We analyze the effect of multitrace deformations in conformal field theories at leading order in a large N approximation. These theories admit a description in terms of a weakly coupled gravity dual. We show how the deformations can be mapped into boundary terms of the gravity theory and how to reproduce the RG equations found in field theory. In the case of doubletrace deformations, and for bulk scalars with masses in the range $-d^2/4<m^2<-d^2/4+1$, the deformed theory flows between two fixed points of the renormalization group, manifesting a resonant behavior at the scale characterizing the transition between the two CFT's. On the gravity side the resonance is mapped into an IR non-normalizable mode (Gamow state) whose overlap with the UV region increases as the dual operator approaches the free field limit. We argue that this resonant behavior is a generic property of large N theories in the conformal window, and associate it to a remnant of the Nambu-Goldstone mode of dilatation invariance. We emphasize the role of nonminimal couplings to gravity and establish a stability theorem for scalar/gravity systems with AdS boundary conditions in the presence of arbitrary boundary potentials and nonminimal coupling.Comment: 14 pages, references added, introduction change

Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry

We use a covariant phase space formalism to give a general prescription for defining Hamiltonian generators of bosonic and fermionic symmetries in diffeomorphism invariant theories, such as supergravities. A simple and general criterion is derived for a choice of boundary condition to lead to conserved generators of the symmetries on the phase space. In particular, this provides a criterion for the preservation of supersymmetries. For bosonic symmetries corresponding to diffeomorphisms, our prescription coincides with the method of Wald et al. We then illustrate these methods in the case of certain supergravity theories in $d=4$. In minimal AdS supergravity, the boundary conditions such that the supercharges exist as Hamiltonian generators of supersymmetry transformations are unique within the usual framework in which the boundary metric is fixed. In extended ${\mathcal N}=4$ AdS supergravity, or more generally in the presence of chiral matter superfields, we find that there exist many boundary conditions preserving ${\mathcal N}=1$ supersymmetry for which corresponding generators exist. These choices are shown to correspond to a choice of certain arbitrary boundary ``superpotentials,'' for suitably defined ``boundary superfields.'' We also derive corresponding formulae for the conserved bosonic charges, such as energy, in those theories, and we argue that energy is always positive, for any supersymmetry-preserving boundary conditions. We finally comment on the relevance and interpretation of our results within the AdS-CFT correspondence.Comment: 45 pages, Latex, no figures, v2: extended discussion of positive energy theorem and explicit form of fermionic generators, references adde