Abstract Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is exactly preserved for anomaly-free theories and thus is completely free from the question of the gauge mode decoupling. In the present paper, we propose yet another lattice formulation sharing this desired property. A particularly unique point in our formulation is that the vertex operator of the dual scalar field, which carries the vector charge of the fermion and the “magnetic charge” in the bosonization, is represented by a “hole” excised from the lattice; this is the excision method formulated recently by Abe et al. in a somewhat different context.

Japan

Okuto Morikawa

Soma Onoda

Hiroshi Suzuki

Yet Another Lattice Formulation of 2D (1) Chiral Gauge Theory via Bosonization David Tong: lectures on gauge theory

We discuss some aspects related to holography of anti–de Sitter (AdS) dyonic hairy black holes, which break the conformal symmetry of the boundary. We use counterterms for the scalar field that satisfies mixed boundary conditions to compute the Euclidean action and dual stress tensor. We apply these results to show that the Cardy-Verlinde formula is not satisfied. However, when the magnetic (or electric) charge vanishes, the conformal symmetry is preserved and the entropy of the black hole can be put in the Cardy-Verlinde form. In our analysis, there is no need of adding extra finite counterterms and, in this particular case, we explicitly show that our results match the ones obtained from using the superpotential as a counterterm.

Chile

Dumitru Astefanesei

David Choque

Jorge Maggiolo

Raúl Rojas

Holography of AdS hairy black holes and Cardy-Verlinde formula

We investigate the phase diagram of a general class of 4-dimensional exact regular hairy planar black holes. For some particular values of the parameters in the moduli potential, these solutions can be embedded in ω-deformed   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 gauged supergravity. We construct the hairy soliton that is the ground state of the theory and show that there exist first order phase transitions.

Andres Anabalon

Peru

Spain

Jose Edelstein

Phase transitions of neutral planar hairy AdS black holes

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 thermodynamically stable asymptotically flat black hole, without imposing artificial conditions corresponding to embedding in a finite box.

Francisco Gómez

Thermodynamically stable asymptotically flat hairy black holes with a dilaton potential

We present a variational formulation of Einstein–Maxwell-dilaton theory in flat spacetime, when the asymptotic value of the scalar field is not fixed. We obtain the boundary terms that make the variational principle well posed and then compute the finite gravitational action and corresponding Brown–York stress tensor. We show that the total energy has a new contribution that depends on the asymptotic value of the scalar field and discuss the role of scalar charges for the first law of thermodynamics. We also extend our analysis to hairy black holes in Anti-de Sitter spacetime and investigate the thermodynamics of an exact solution that breaks the conformal symmetry of the boundary.

Romina Ballesteros

Scalar charges and the first law of black hole thermodynamics

We construct exact hairy AdS soliton solutions in Einstein-dilaton gravity theory. We examine their thermodynamic properties and discuss the role of these solutions for the existence of first order phase transitions for hairy black holes. The negative energy density associated to hairy AdS solitons can be interpreted as the Casimir energy that is generated in the dual filed theory when the fermions are antiperiodic on the compact coordinate.

Andrés Anabalón

Hairy AdS solitons

We construct concrete counterterms of the Balasubramanian-Kraus type for Einstein-scalar theories with designer gravity boundary conditions in AdS 4 , so that the total action is finite on-shell and satisfy a well defined variational principle. We focus on scalar fields with the conformal mass m 2 = −2 l −2 and show that the holographic mass matches the Hamiltonian mass for any boundary conditions. We compute the trace anomaly of the dual field theory in the generic case, as well as when there exist logarithmic branches of non-linear origin. As expected, the anomaly vanishes for the boundary conditions that are AdS invariant. When the anomaly does not vanish, the dual stress tensor describes a thermal gas with an equation of state related to the boundary conditions of the scalar field. In the case of a vanishing anomaly, we recover the dual theory of a massless thermal gas. As an application of the formalism, we consider a general family of exact hairy black hole solutions that, for some particular values of the parameters in the moduli potential, contains solutions of four-dimensional gauged N = 8 $$ \mathcal{N}=8 $$ supergravity and its ω -deformation. Using the AdS/CFT duality dictionary, they correspond to triple trace deformations of the dual field theory.

Germany

Cristián Martínez

Trace anomaly and counterterms in designer gravity

We investigate the thermodynamics of a general class of exact 4-dimensional asymptotically Anti-de Sitter hairy black hole solutions and show that, for a fixed temperature, there are small and large hairy black holes similar to the Schwarzschild–AdS black hole. The large black holes have positive specific heat and so they can be in equilibrium with a thermal bath of radiation at the Hawking temperature. The relevant thermodynamic quantities are computed by using the Hamiltonian formalism and counterterm method. We explicitly show that there are first order phase transitions similar to the Hawking–Page phase transition.