A note on theta dependence
arXiv:hep-th/0111117 · doi:10.1016/S0370-2693(02)01261-3
Abstract
The dependence on the topological theta angle term in quantum field theory is usually discussed in the context of instanton calculus. There the observables are 2 pi periodic, analytic functions of theta. However, in strongly coupled theories, the semi-classical instanton approximation can break down due to infrared divergences. Instances are indeed known where analyticity in theta can be lost, while the 2 pi periodicity is preserved. In this short note we exhibit a simple two dimensional example where the 2 pi periodicity is lost. The observables remain periodic under the transformation theta -> theta + 2 k pi for some k >= 2. We also briefly discuss the case of four dimensional N=2 supersymmetric gauge theories.
6 pages; v2: a couple of clarifying sentences added; v3: references added