Vacuum polarization for compactified QED4+1 in a magnetic flux background

Full text. Quantum field theory models with compactified dimensions have been used to describe different physical phenomena, which range from finite size effects in critical phenomena, to particle physics models. Here, since the pioneering works of Kaluza and Klein, extra dimensions have played an important role to search for methods to unify the fundamental interactions and to describe a wide range of physical situations; to name a few: alternative solutions to the hierarchy problem, physics at the TeV scale, and particle physics models where the extra dimensions play an important role to implement the unification of fundamental interactions. An interesting yet simple example of this, corresponds to the compactification of one dimension in an RD Euclidean spacetime, such that the topology of the resulting manifold M is that of RD-1 x S1, i.e., circular compactification'. Although the compelling features that emerge in this situation have been studied using several different techniques in the literature, one can take advantage of a (formal) common feature; indeed, they share many properties with the imaginary-time formulation of quantum field theory at finite temperature. This allows one, for example, to take advantage of the many well-known methods and results developed in this context, such as Feynman diagrams and renormalization techniques, to import them to the case under consideration. Following this rationale we evaluate one-loop effects for QED4+1 compactified to R4 x S1, in a non-trivial vacuum for the gauge field, such that a non-vanishing magnetic flux is encircled along the extra dimension. We obtain the vacuum polarization tensor and evaluate the exact parity breaking term, presenting the results from the point of view of the effective 3 + 1 dimensional theory. (author)