Induced fermionic current densities by magnetic flux in higher dimensional cosmic string spacetime

In this paper, we analyze the vacuum fluctuations of quantum fermionic current densities, (jA(x)), induced by a magnetic flux running along the core of the conical space produced by the presence of cosmic string, in a (1 + d)-dimensional bulk, for 2 ≤ d ≤ 5. In order to develop this investigation, we construct an expression for the fermionic propagator, which can be applied for those different dimensions of the spacetime. Two specific analyses for the induced current densities are presented: (i) for massless fields in three and four dimensions and (ii) for massive fields in all dimensions considered. In the latter, specific values for the parameters which codify the presence of the cosmic string and the fractional part of the ratio of the magnetic flux to the quantum one are considered. Although being a very special situation and somewhat unnatural, the corresponding analysis of induced fermionic current densities under this circumstance may shed light on the qualitative behavior of these quantities in a more general situation.