Trace and chiral anomalies in string and ordinary field theory from Feynman diagrams for non-linear sigma models Original Research Article

We write general one-loop anomalies of string field theory as path integrals on a torus for the corresponding non-linear sigma model. This extends the work of Alvarez-Gaumé and Witten from quantum mechanics to two dimensions. Higher world-volume loops contribute in general to non-topological anomalies and a formalism to compute these is developed. We claim that (i) for general anomalies one should not use the propagator widely used in string theory but rather the one obtained by generalization from quantum mechanics, but (ii) for chiral anomalies both propagators give the same result. As a check of this claim in a simpler model we compute trace anomalies in quantum mechanics. The propagator with a center-of-mass zero mode indeed does not give the correct result for the trace anomaly while the propagator for fluctuations qi(τ) satisfying qi (τ = −1) = qi (τ = 0) = 0 yields in d = 2 and d = 4 dimensions the correct results from two- and three-loop graphs.