Vacuum energy, temperature corrections and heat kernel coefficients in $(D + 1)$-dimensional spacetimes with nontrivial topology

Abstract: In this work we make use of the generalized zeta function technique to investigate the vacuum energy, temperature corrections and heat kernel coefficients associated with a scalar field under a quasiperiodic condition in a $(D+1)$-dimensional conical spacetime. In this scenario we find that the renormalized vacuum energy, as well as the temperature corrections, are both zero. The nonzero heat kernel coefficients are the ones related to the usual Euclidean divergence, and also to the nontrivial aspects of the quaisperiodically identified conical spacetime topology. An interesting result that arises in this configuration is that for some values of the quasiperiodic parameter, the heat kernel coefficient associated with the nontrivial topology vanishes. In addition, we also consider the scalar field in a $(D+1)$-dimensional spacetime formed by the combination of a conical and screw dislocation topological defects. In this case, we obtain a nonzero renormalized vacuum energy density and its corresponding temperature corrections. Again, the nonzero heat kernel coefficients found are the ones related to the Euclidean and nontrivial topology divergences. For $D=3$ we explicitly show, in the massless scalar field case, the limits of low and high temperatures for the free energy. In the latter, we show that the free energy presents a classical contribution.