Fermionic vacuum currents in topologically nontrivial braneworlds: Twobrane 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. The influence of the latter on the VEV is of the AharonovBohm type. 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 branefree and braneinduced 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 energymomentum tensor, the VEV of the current density is finite on the branes. Applications are given to higherdimensional generalizations of the RandallSundrum models with two branes and with toroidally compact subspace. The features of the fermionic current are discussed in odddimensional parity and timereversal symmetric models. The corresponding results for threedimensional 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.
 Publication:

Physical Review D
 Pub Date:
 February 2020
 DOI:
 10.1103/PhysRevD.101.045020
 arXiv:
 arXiv:1907.13379
 Bibcode:
 2020PhRvD.101d5020B
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 33 pages, 7 figures, PACS numbers: 04.62.+v, 03.70.+k, 98.80.k, 61.46.Fg