Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

TL;DR

This paper studies how a brane and cosmic string in 4+1D AdS spacetime affect vacuum fermionic currents, revealing decay behaviors and boundary condition effects relevant for braneworld models like Randall-Sundrum.

Contribution

It provides a detailed analysis of vacuum fermionic currents in AdS braneworlds with cosmic strings, including boundary condition effects and decay behaviors, extending previous Minkowski space results.

Findings

The azimuthal current density is the only nonzero component.

Brane-induced current vanishes on the string and near it.

Decay of the current density is power-law at large distances in AdS.

Abstract

We investigate the effects of a brane and magnetic-flux-carrying cosmic string on the vacuum expectation value (VEV) of the current density for a charged fermionic field in the background geometry of 4+1 dimensional anti-de Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and the cosmic string is orthogonal to the brane. Two types of boundary conditions are considered on the brane that include the MIT bag boundary condition and the boundary conditions in Z2-symmetric braneworld models. The brane divides the space into two regions with different properties of the vacuum state. The only nonzero component of the current density is along the azimuthal direction and in both the regions the corresponding VEV is decomposed into the brane-free and brane-induced contributions. The latter vanishes on the string and near the string the total current is dominated by the brane-free part. At large distances from the string and in the region between the brane and AdS horizon the decay of the brane-induced current density, as a function of the proper distance, is power-law for both massless and massive fields. For a massive field this behavior is essentially different from that in the Minkowski bulk. In the region between the brane and AdS boundary the large-distance decay of the current density is exponential. Depending on the boundary condition on the brane, the brane-induced contribution is dominant or subdominant in the total current density at large distances from the string. By using the results for fields realizing two inequivalent irreducible representations of the Clifford algebra, the vacuum current density is investigated in C- and P-symmetric fermionic models. Applications are given for a cosmic string in the Randall-Sundrum-type braneworld model with a single brane.