Fermionic vacuum currents in topologically nontrivial braneworlds: Two-brane geometry

Abstract

The vacuum expectation value (VEV) of the fermionic current density is investigated in the geometry of two parallel branes in locally AdS spacetime with a part of spatial dimensions compactified to a torus. Along the toral dimensions quasiperiodicity conditions are imposed with general phases and the presence of a constant gauge field is assumed. Different types of boundary conditions are discussed on the branes, including the bag boundary condition and the conditions arising in $Z_{2}$-symmetric braneworld models. Nonzero vacuum currents appear along the compact dimensions only. In the region between the branes they are decomposed into the brane-free and brane-induced contributions. Both these contributions are periodic functions of the magnetic flux enclosed by compact dimensions with the period equal to the flux quantum. Depending on the boundary conditions, the presence of the branes can either increase or decrease the vacuum current density. For a part of boundary conditions, a memory effect is present in the limit when one of the branes tends to the AdS boundary. Unlike to the fermion condensate and the VEV of the energy-momentum tensor, the VEV of the current density is finite on the branes. Applications are given to higher-dimensional generalizations of the Randall-Sundrum models with two branes and with toroidally compact subspace. The features of the fermionic current are discussed in odd-dimensional parity and time-reversal symmetric models. The corresponding results for three-dimensional spacetime are applied to finite length curved graphene tubes threaded by a magnetic flux. It is shown that a nonzero current density can also appear in the absence of the magnetic flux if the fields corresponding to two different points of the Brillouin zone obey different boundary conditions on the tube edges.