arXiv subjects

Ankur

Publications and source records attributed to Ankur.

5 recordsLinked to original sources

arXiv2026

Dressing and Screening in Anti-de Sitter

Motivated by a question of defining gauge-invariant observables in cosmology and by the close connection between perturbation theory in de Sitter (dS) and Anti-de Sitter (AdS), we study scalar electrodynamics in AdS in setups that are largely unexplored but relevant for dS physics. For photons with standard (Dirichlet) boundary conditions, we analyze charged scalars whose boundary conditions break the $U(1)$ symmetry. This leads to a nonstandard Higgs mechanism in which the gauge field acquires a one-loop mass without a classical vacuum expectation value. Using recent advances in perturbation theory in AdS, we compute this mass explicitly and evaluate charged-scalar four-point functions. We also provide an alternative derivation based on boundary Ward identities. For photons with alternate (Neumann) boundary conditions, where local charged operators are not gauge invariant, we construct physical observables by dressing charged fields with geodesic Wilson lines. These dressed operators have well-behaved conformal properties and unphysical photon modes decouple from their correlation functions. Explicit one-loop computations further reveal the decoupling of boundary field strengths, for which we provide a nonperturbative argument based on higher-form symmetry. Along the way, we explain the physical consequences of spontaneous breaking of higher-form symmetry in AdS, including the role of the tilt operator, the relation between one-form symmetry and endpoints of Wilson lines at the boundary, and a generalized-symmetry interpretation of conserved currents dual to bulk gauge fields.

hep-th↗

arXiv2024

Finite Element Simulation of Modified Poisson-Nernst-Planck/Navier-Stokes Model for Compressible Electrolytes under Mechanical Equilibrium

This work presents a finite element method for a modified Poisson-Nernst-Planck/Navier-Stokes (PNP/NS) model under the mechanical equilibrium, developed for compressible electrolytes. Another key contribution of this work is the reduction of the equilibrium system to a modified Poisson-Boltzmann system. The proposed numerical scheme is capable of handling both compressible and incompressible regimes by employing a bulk modulus parameter, which governs the fluid's compressibility and enables seamless transition between these regimes. To emphasize practical relevance, we discuss the implications of compressible electrolytes in the context of double-layer capacitance behavior. We also conduct numerical simulations over various domains to demonstrate its applicability under various operating conditions, including temperature fluctuations and variations in the bulk modulus. The numerical results validate the accuracy and robustness of our computational scheme and demonstrate that the observed limiting behavior for the incompressible regime aligns with the theoretical trends anticipated by Dreyer et al. [39].

math.NA↗

arXiv2024

Conformal Finite Element Methods for Nonlinear Rosenau-Burgers-Biharmonic Models

We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence, and uniqueness statements of the corresponding variational methods. We also obtain optimal error estimates of the semidiscrete scheme in corresponding B\^ochner spaces. Finally, we construct a fully discrete scheme through a backward Euler discretization of the time derivative, and prove well-posedness statements for this fully discrete scheme. Our findings show that the mixed approach removes some theoretical impediments to analysis and is numerically easier to implement. We provide numerical simulations for the mixed formulation approach using $C^0$ Taylor-Hood finite elements on several domains. Our numerical results confirm that the algorithm has optimal convergence in accordance with the observed theoretical results.

math.NA↗

arXiv2023

Scalar QED in AdS

We consider scalar QED with $N_f$ flavors in AdS$_D$. For $D<4$ the theory is strongly-coupled in the IR. We use the spin 1 spectral representation to compute and efficiently resum the bubble diagram in AdS, in order to obtain the exact propagator of the photon at large $N_f$. We then apply this result to compute the boundary four-point function of the charged operators at leading order in $1/N_f$ and exactly in the coupling, both in the Coulomb and in the Higgs phase. In the first case a conserved current is exchanged in the four-point function, while in the second case the current is absent and there is a pattern of double-trace scaling dimension analogous to a resonance in flat space. We also consider the BCFT data associated to the critical point with bulk conformal symmetry separating the two phases. Both in ordinary perturbation theory and at large $N_f$, in integer dimension $D= 3$ an IR divergence breaks the conformal symmetry on the boundary by inducing a boundary RG flow in a current-current operator.

hep-th↗

arXiv2021

Dynamic noncommutative BTZ black holes

We have studied the charged BTZ black holes in noncommutative spaces arising from two independent approaches. First, by using the Seiberg-Witten map followed by a dynamic choice of gauge in the Chern-Simons gauge theory. Second, by inducing the fuzziness in the mass and charge by a Lorentzian distribution function with the width being the same as the minimal length of the associated noncommutativity. In the first approach, we have found the existence of non-static and non-stationary BTZ black holes in noncommutative spaces for the first time in the literature, while the second approach facilitates us to introduce a proper bound on the noncommutative parameter so that the corresponding black hole becomes stable and physical. We have used a contemporary tunneling formalism to study the thermodynamics of the black holes arising from both of the approaches and analyze their behavior within the context.

hep-th↗