KAPPA-ANOMALIES AND SPACE-TIME SUPERSYMMETRY IN THE GREEN-SCHWARZ HETEROTIC SUPERSTRING

The computation of K-anomalies in the Green-Schwarz heterotic superstr ing sigma-model and the corresponding Wess-Zumino consistency conditio n constitute a powerful alternative approach for the derivation of man ifestly supersymmetric string effective actions. With respect to the b eta-function approach this technique presents the advantage that a res ult which is obtained with the computation of beta-functions at n loop s can be obtained through the calculation of kappa-anomalies at n - 1 loops. In this paper we derive by a direct one-loop perturbative compu tation the kappa-anomaly associated to the Yang-Mills Chem-Simons thre eform and, for the first time, the one associated to the Lorentz Chem- Simons threeform. In the calculation we shall use a convenient set of constraints for the pure N = 1, D = 10 supergravity theory which is al gebraically identical to the standard set of constraints for the pure N = 1, D = 10 super Yang-Mills theory. Contrary to what is often state d in the literature we show that the Lorentz kappa-anomaly gets contri butions from the integration over both the fermionic and bosonic degre es of freedom of the string. A careful analysis of the absolute coeffi cients of all these anomalies reveals that they can be absorbed by set ting dH = alpha'/4(tr F-2 - tr R(2)), where alpha' is the string tensi on, the expected results. We show that this relation ensures also the absence of gauge and Lorentz anomalies in the sigma-model effective ac tion. Moreover, the consistency condition of the kappa-anomalies ensur es the closure of the SUSY algebra in the Bianchi identities. We exhib it the presence of infrared divergences in the heterotic string sigma model, which are due to the presence of the d = 2 scalar massless fiel ds of the string, and present a conjecture for their cancellation whic h is intimately related to the locality and Wess-Zumino consistency of the kappa-anomalies.