We study soliton and black hole solutions with scalar hair in AdS in a theory with a Maxwell field and a charged scalar field with double trace boundary conditions, which can trigger the dual boundary theory to become a superconductor. We investigate the phase diagram as a function of the temperature $\textit{T}$ and of the double trace coupling $\textit{κ}$ and we find a rich pattern of phase transitions, which can be of the Hawking-Page kind or can be due to the condensation of the order parameter. We also find a transition between vortex solutions and the zero temperature limit of the black hole for a critical value of the double trace coupling $\textit{κ}$. The Little-Park periodicity is realized for the dual of the black hole solution with hair as a shift in the winding number and in the gauge field.

Italy

Roberto Auzzi

Stefano Bolognesi

Giuseppe Nardelli

Chile

Gianni Tallarita

Japan

Nicolò Zenoni

Solitonic vortices and black holes with vortex hair in AdS

We couple Fermions to the isospinning (2+1) baby-skyrme model. We show that consistent rotationally invariant localised solutions can be found but the Fermionic solutions to the equations of motion are not in general eigenstates of the Hamiltonian. These do however become full eigenstates in a particular limit. We also find the corresponding Fermionic eigenstates of the Hamiltonian, for which our Fermion ansatz is also well suited. For localised Fermionic states, a novel constraint on the internal isospin frequency exists. Throughout our studies, we include the backreaction of the Fermions on the baby-skyrmion.

Marco Barsanti

Rotationally invariant isospinning baby-skyrmions dressed by fermions

In the presence of a scalar hair perturbation, the Cauchy horizon of a Reissner-Nordström black hole disappears and is replaced by the rapid collapse of the Einstein-Rosen bridge, which leads to a Kasner singularity [1, 2]. We study the time-dependence of holographic complexity, both for the volume and for the action proposals, in a class of models with hairy black holes. Volume complexity can only probe a portion of the black hole interior that remains far away from the Kasner singularity. We provide numerical evidence that the Lloyd bound is satisfied by the volume complexity rate in all the parameter space that we explored. Action complexity can instead probe a portion of the spacetime closer to the singularity. In particular, the complexity rate diverges at the critical time t  c  for which the Wheeler-DeWitt patch touches the singularity. After the critical time the action complexity rate approaches a constant. We find that the Kasner exponent does not directly affect the details of the divergence of the complexity rate at t = t  c  and the late-time behaviour of the complexity. The Lloyd bound is violated by action complexity at finite time, because the complexity rate diverges at t = t  c . We find that the Lloyd bound is satisfied by the asymptotic action complexity rate in all the parameter space that we investigated.

Israel

France

Eliezer Rabinovici

Fidel Schaposnik Massolo

On the time dependence of holographic complexity for charged AdS black holes with scalar hair

The dynamics of both global and local vortices with non-Abelian orientational moduli is investigated in detail. Head-on collisions of these vortices are numerically simulated for parallel, anti-parallel and orthogonal internal orientations where we find interesting dynamics of the orientational moduli. A detailed study of the inter-vortex force is provided and a phase diagram separating Abelian and non-Abelian vortex types is constructed. Some results on scatterings with non-zero impact parameter and multi-vortex collisions are included.

Minoru Eto

United States

Adam Peterson

Dynamics of global and local vortices with orientational moduli

We study the baby Skyrme model in (2+1)-dimensions built on a finite cylinder. To this end, we introduce a consistent ansatz which is able to reduce the complete set of field equations to just one equation for the profile function for arbitrary baryon charge. Many analytic solutions both with and without the inclusion of the effects of the minimal coupling with the Maxwell field are constructed. The baby skyrmions appear as a sequence of rings along the cylinder, leading to a periodic shape in the baryon density. Linear stability and other physical properties are discussed. These analytic gauged baby Skyrmions generate a persistent U(1) current which cannot be turned off continuously as it is tied to the topological charge of the baby Skyrmions themselves. In the simplest non-trivial case of a gauged baby Skyrmion, a very important role is played by the Mathieu equation with an effective coupling constant which can be computed explicitly. These configurations are a very suitable arena to test resurgence in a non-integrable context.

Fabrizio Canfora

Analytic baby skyrmions at finite density

We study two-dimensional weighted   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,   <math> <mover> <mi>N</mi> <mo>˜</mo> </mover> </math>  $$ \tilde{N} $$ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,   <math> <mover> <mi>N</mi> <mo>˜</mo> </mover> </math>  $$ \tilde{N} $$ ) has N charges +1 and   <math> <mover> <mi>N</mi> <mo>˜</mo> </mover> </math>  $$ \tilde{N} $$  charges −1 fields. As well-known, at   <math> <mover> <mi>N</mi> <mo>˜</mo> </mover> </math>  $$ \tilde{N} $$  = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold.

China

Jin Chen

Chao-Hsiang Sheu

Mikhail Shifman

Russia

Alexei Yung

Long way to Ricci flatness

We explore vorton solutions in the Witten’s $$U(1) \times U(1)$$ <math><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math>  model for cosmic strings and in a modified version $$U(1) \times SO(3)$$ <math><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></math>  obtained by introducing a triplet of non-Abelian fields to condense inside the string. We restrict to the case in which the unbroken symmetry in the bulk remains global. The vorton solutions are found numerically for certain choices of parameters and compared with an analytical solutions obtained in the thin vorton limit. We also discuss the vorton decay into Q-rings (or spinning Q-balls) and, to some extent, the time dependent behavior of vortons above the charge threshold.

Canada

Peter Bedford

Vortons with Abelian and non-Abelian currents and their stability

We investigate vortex lattice solutions in a holographic superconductor model in asymptotically AdS4 spacetime which includes the gravitational backreaction of the vortex. The circular cell approximation, which is known to give a good result for several physical quantities in the Ginzburg-Landau model, is used. The critical magnetic fields and the magnetization curve are computed. The vortex lattice profiles are compared to expectations from the Abrikosov solution in the regime nearby the upper critical magnetic field H2c for which superconductivity is lost.

The holographic vortex lattice using the circular cell method

We study holographic subregion volume complexity for a line segment in the AdS3 Vaidya geometry. On the field theory side, this gravity background corresponds to a sudden quench which leads to the thermalization of the strongly-coupled dual conformal field theory. We find the time-dependent extremal volume surface by numerically solving a partial differential equation with boundary condition given by the Hubeny-Rangamani- Takayanagi surface, and we use this solution to compute holographic subregion complexity as a function of time. Approximate analytical expressions valid at early and at late times are derived.

Belgium

On volume subregion complexity in Vaidya spacetime

We study a fully back-reacted non-abelian vortex solution in an extension of the holographic superconductor setup. The thermodynamic properties of the vortex are computed. We show that, in some regime of parameters, the non-abelian vortex solution has a lower free energy than a competing abelian vortex solution. The solution is dual to a finite-temperature perturbed conformal field theory with a topological defect, on which operators related to the Goldstone modes of a spontaneously broken symmetry are localized. We compute numerically the retarded Green function of these operators and we find, in the classical approximation in the bulk, a gapless ℂℙ1 excitation on the vortex world line.