TRACE AND CHIRAL ANOMALIES IN STRING AND ORDINARY FIELD-THEORY FROM FEYNMAN DIAGRAMS FOR NONLINEAR SIGMA-MODELS

We write general one-loop anomalies of string field theory as path int egrals on a torus for the corresponding non-linear sigma model. This e xtends the work of Alvarez-Gaume 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 propaga tor widely used in string theory but rather the one obtained by genera lization from quantum mechanics, but (ii) for chiral anomalies both pr opagators 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 resul t for the trace anomaly while the propagator for fluctuations q(i)(tau ) satisfying q(i)(tau = -1) = q(i)(tau = 0) = 0 yields in d = 2 and d = 4 dimensions the correct results from two-and three-loop graphs. We then return to heterotic string theory and calculate the contributions to the anomaly from the different spin structures for d = 2. We obtai n agreement with the work of Pilch, Schellekens and Warner and that of Li in the sector with space-time fermions. In the other sectors, wher e no explicit computations have been performed in the past and for whi ch one needs higher loops, we find a genuine divergence, whose interpr etation is unclear to us. We discuss whether or not this leads to a ne w anomaly. (C) 1998 Published by Elsevier Science B.V.