Induced Cosmological Constant in Braneworlds with Compact Dimensions

Abstract

We investigate the cosmological constant induced by quantum fluctuations of a bulk charged scalar field on a brane in background of locally anti-de Sitter spacetime with toroidally compact spatial dimensions. Along compact dimension quasiperiodicity conditions are imposed with general phases and, in addition, the presence of a constant gauge field is assumed. The latter gives rise to Aharonov-Bohm type effect on the characteristics of the scalar vacuum. The renormalization of the vacuum energy density on the brane is done by making use of the generalized zeta function technique. The behavior of the cosmological constant is studied as a function of the location of the brane, of the length of the compact dimensions and of the magnetic flux enclosed by the compact dimension. In particular, it is shown that the cosmological constant is a periodic function of the magnetic flux with the period equal to the flux quantum.