Induced vacuum currents in anti-de Sitter space with toral dimensions

TL;DR

This paper studies vacuum-induced currents for a charged scalar field in anti-de Sitter space with compact dimensions, revealing how gauge fields and geometry influence quantum vacuum effects.

Contribution

It provides a detailed analysis of vacuum currents in AdS space with toroidal compactification, including effects of gauge fields and boundary conditions, highlighting differences from Minkowski space.

Findings

Vacuum current density is periodic in gauge flux with flux quantum period.

Current vanishes at the AdS boundary and relates conformally to Minkowski results near the horizon.

For large compact dimensions, the current decays as a power-law, unlike exponential decay in Minkowski space.

Abstract

We investigate the Hadamard function and the vacuum expectation value of the current density for a charged massive scalar field on a slice of anti-de Sitter (AdS) space described in Poincar\'{e} coordinates with toroidally compact dimensions. Along compact dimensions periodicity conditions are imposed on the field with general phases. Moreover, the presence of a constant gauge field is assumed. The latter gives rise to Aharonov-Bohm-like effects on the vacuum currents. The current density along compact dimensions is a periodic function of the gauge field flux with the period equal to the flux quantum. It vanishes on the AdS boundary and, near the horizon, to the leading order, it is conformally related to the corresponding quantity in Minkowski bulk for a massless field. For large values of the length of the compact dimension compared with the AdS curvature radius, the vacuum current decays as power-law for both massless and massive fields. This behavior is essentially different from from the corresponding one in Minkowski background, where the currents for a massive field are suppressed exponentially.