Infrared divergences of toroidal effective potentials

Abstract

In the calculations of the contributions of massless fields to 1-loop effective potentials on spacetimes of the form Rm*Td, it is known that infrared divergences can only be avoided if the Euclidean space dimension m is greater than 2. In recent papers dealing with vanishing gauge background, such infrared divergences are confined to the toroidal zero momentum mode, and it has been claimed that this mode should therefore be ignored in the subsequent analysis. However, as there can exist nontrivial 'flat' gauge vacua on nonsimply connected manifolds, then such backgrounds must be included in any analysis on the torus. As a consequence, it is shown that, even if the infrared divergent zero momentum mode is discarded, the remaining contributions to the 1-loop potential still exhibit poor infrared behaviour at certain nonzero gauge background configurations. As a result, any conclusions drawn previously on the assumption of finiteness of the nonzero mode contributions must be considered invalid.