Motivated by the potential experimental relevance of magnetically affected heavy-quark diffusion, we consider here a five-dimensional nonlinear Einstein-Born-Infeld-dilaton model to not only holographically model the QCD thermodynamics in a magnetic background but also to probe the charged inner structure of a heavy quarkonium. The dual model’s gravitational equations of motion can be solved in analytical form via the potential reconstruction method. Using a variety of tools—spectral functions, hydrodynamic expansions, or hanging strings—we study the anisotropic diffusion constants and heavy-quark number susceptibility, each time reporting closed form expressions.

India

Siddhi Swarupa Jena

Arpan Bhattacharjee

Belgium

David Dudal

Subhash Mahapatra

Probing quarkonium diffusion in a magnetized quark-gluon plasma

We present a self-consistent dynamical holographic quantum chromodynamics (QCD) model to investigate the mass spectra and melting behavior of heavy and exotic mesons at finite temperature and finite density. Our approach is based on the Einstein-Maxwell-dilaton (EMD) framework and incorporates an elsewhere already introduced, albeit by hand, phenomenological nonquadratic dilaton profile. This allows one to capture the nonlinear Regge trajectories of heavy-flavor mesons and model certain exotic states. We show how to construct such models by actually solving the coupled Einstein, Maxwell, and dilaton field equations, ensuring mathematical self-consistency to replace any ad hoc input. At finite temperature, we analyze the confinement-deconfinement transition via a Hawking-Page phase transition. We compute the spectral functions, revealing the sequential melting of quarkonia as the temperature is increased. Extending to finite density, we explore the impact of baryon chemical potential on meson stability, showing significant modifications in spectral peaks and effective potentials that indicate a more rapid melting of mesonic states as the chemical potential increases in the deconfined phase. The dual of the small/large black hole transition now indicates toward a first order phase transition line ending at a second order critical point. Interestingly, the spectral functions smoothly cross this phase transition line.

Brazil

Bruno Toniato

Roldao da Rocha

Holographic QCD model for heavy and exotic mesons at finite density: A self-consistent dynamical approach

We investigate the role of both magnetic field and chemical potential on the emergence of chaotic dynamics in the quantum chromodynamics (QCD) confining string from the holographic principle. An earlier developed bottom-up model of Einstein-Maxwell-dilaton gravity, which mimics QCD features quite well, is used. The qualitative information about the chaos is obtained using the Poincaré sections and Lyapunov exponents. We find signatures of chaos in energetically disfavored string configurations, that are closer to the horizon, whereas no chaos is observed in energetically favored string configurations that are away from the horizon. Our results depend quite strongly on the frame we consider in the analysis. In the string frame, the chemical potential and the magnetic field suppress the chaotic dynamics in both parallel and perpendicular orientations of the string with respect to the magnetic field. Meanwhile, in the Einstein frame, the magnetic field suppresses/enhances the chaotic dynamics when the string is orientated perpendicular/parallel to the magnetic field, while the chemical potential enhances the chaotic dynamics for both orientations. The reported Lyapunov exponents are consistent with a classical analogue of the Maldacena-Shenker-Stanford bound in the parameter space of the model and we find it to be always satisfied in both frames.

Bhaskar Shukla

Jasper Nongmaithem

Interplay of magnetic field and chemical potential induced anisotropy and frame dependent chaos of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>Q</mi><mover accent="true"><mrow><mi>Q</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow></math> pair in holographic QCD

Recently, dynamical edge modes (DEM) in Maxwell theory have been constructed using a specific local boundary condition on the horizon. We discuss how to enforce this boundary condition on an infinite parallel plate in the QED vacuum by introducing Lagrange multiplier fields into the action. We carefully introduce appropriate boundary ghosts to maintain BRST invariance. Explicit correspondence of this BRST extended theory with the original DEM formulation is discussed, both directly, and through the correspondence between edge modes and Wilson lines attached to the boundary surface. We then use functional methods to calculate the Casimir energy for the first time with DEM boundary conditions imposed on two infinite parallel plates, both in generalized Coulomb and linear covariant gauge. Depending on the gauge, different fields are contributing, but, after correctly implementing the BRST symmetry, we retrieve the exact same Casimir energy as for two perfectly conducting parallel plates.

Chile

Fabrizio Canfora

Thomas Oosthuyse

Italy

Luigi Rosa

Sebbe Stouten

Dynamical edge modes in Maxwell theory from a BRST perspective, with an application to the Casimir energy

We reconsider the equivalence theorem from an algebraic viewpoint, using an extended Becchi-Rouet-Stora-Tuytin symmetry. This version of the equivalence theorem is then used to reexpress the Abelian Higgs model action, originally written in terms of undesirable gauge variant field excitations, in terms of gauge-invariant, physical variables, corresponding to the Fröhlich-Morchio-Strocchi composite operators in the original field formulation. Although the ensuing action encompasses an infinite number of vertices and appears to be nonrenormalizable from the power counting viewpoint, it nevertheless is renormalizable, thanks to the hidden equivalence with the original model. Hence, manifestly gauge-invariant computations are possible. We present an explicit illustration in terms of the gauge-invariant scalar field, its Green’s function and corresponding pole mass.

Bram Boeykens

Equivalence theorem at work: Manifestly gauge-invariant Abelian Higgs model physics

We generalize the potential reconstruction method to set up a dynamical Einstein-Born-Infeld-dilaton model, which we then use to study holographic quarkonium melting in an external magnetic field. The non-linear nature of the model allows to couple the magnetic field to the quarkonium inner structure without having to introduce back-reacting charged flavour degrees of freedom. The magnetic field dependent melting temperature is computed from the spectral functions and suggests a switch from inverse magnetic to magnetic catalysis when the magnetic field increases. We also discuss the differences due to the anisotropy brought in by the external field.

Siddhi Jena

Jyotirmoy Barman

A dynamical Einstein-Born-Infeld-dilaton model and holographic quarkonium melting in a magnetic field

Using functional integral methods, we study the Casimir effect for the case of two infinite parallel plates in the QED vacuum, with (different) perfect electromagnetic boundary conditions applied to both plates. To enforce these boundary conditions, we add two Lagrange multiplier fields to the action. We subsequently recover the known Casimir energy in two ways: once directly from the path integral and once as the vacuum expectation value of the 00 component of the energy-momentum tensor. Comparing both methods, we show that the energy-momentum tensor must be modified and that it picks up boundary contributions as a consequence. We also discuss electromagnetic duality invariance of the theory and its interplay with the boundaries by generalizing the Deser-Teitelboim implementation of the duality transformation.

Aaron Gobeyn

Vietnam

David Vercauteren

Casimir energy with perfect electromagnetic boundary conditions and duality: A field-theoretic approach

We study the relationship between the standard or extended thermodynamic phase structure of various anti–de Sitter black holes and the Lyapunov exponents associated with the null and timelike geodesics. We consider dyonic, Bardeen, Gauss-Bonnet, and Lorentz-symmetry breaking massive gravity black holes and calculate the Lyapunov exponents of massless and massive particles in unstable circular geodesics close to the black hole. We find that the thermal profile of the Lyapunov exponents exhibits distinct behavior in the small and large black hole phases and can encompass certain aspects of the van der Waals type small/large black hole phase transition. We further analyze the properties of Lyapunov exponents as an order parameter and find that its critical exponent is <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>, near the critical point for all black holes considered here.

Pranaya Pratik Das

Interplay between the Lyapunov exponents and phase transitions of charged AdS black holes

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 the possibility to obtain a massive Landau gauge, based on the local composite operator effective action framework combined with the Zimmermann reduction of couplings prescription. As a way to deal with the gauge ambiguity, we check that the ghost propagator remains positive, a necessary condition for gluon field configurations beyond the Gribov region to be negligible. We pay attention to the Becchi-Rouet-Stora-Tyutin invariance of the construction, allowing for a future generalization to a class of massive linear covariant gauges. As a litmus test, we compare our predictions to the lattice data for the two-point functions in Landau gauge introducing the “dynamically infrared-safe” renormalization scheme, including the renormalization group optimization of both the gap equation and the two-point functions. We also discuss the relation to and differences with the Curci-Ferrari model, the usefulness of which in providing an effective perturbative description of nonperturbative Yang-Mills theories became clear during recent years.

Giorgio Comitini

Tim De Meerleer

Silvio Paolo Sorella

Dynamically massive linear covariant gauges: Setup and first results