Non-local Probes in Holographic Theories with Momentum Relaxation

TL;DR

This paper investigates how momentum relaxation in holographic theories, introduced via scalar fields with linear profiles, affects entanglement entropy, Wilson loops, and phase transitions, revealing universal corrections and increased inter-object forces.

Contribution

It provides the first detailed analysis of non-local probes in holographic models with momentum relaxation, showing universal and non-universal corrections to entanglement measures and phase transitions.

Findings

Universal terms of entanglement entropy are corrected depending on entangling region geometry.

Momentum relaxation causes phase transitions to occur at smaller separations and critical lengths.

Force between external objects increases with the momentum relaxation parameter.

Abstract

We consider recently introduced solutions of Einstein gravity with minimally coupled massless scalars. The geometry is homogeneous, isotropic and asymptotically anti de-Sitter while the scalar fields have linear spatial-dependent profiles. The spatially-dependent marginal operators dual to scalar fields cause momentum dissipation in the deformed dual CFT. We study the effect of these marginal deformations on holographic entanglement measures and Wilson loop. We show that the structure of the universal terms of entanglement entropy for d(>2)-dim deformed CFTs is corrected depending on the geometry of the entangling regions. In d = 2 case, the universal term is not corrected while momentum relaxation leads to a non-critical correction. We also show that decrease of the correlation length causes: the phase transition of holographic mutual information to happen at smaller separations and the confinement/deconfinement phase transition to take place at smaller critical lengths. The effective potential between point like external objects also gets corrected. We show that the strength of the corresponding force between these objects is an increasing function of the momentum relaxation parameter.