κ-Anomalies and space-time supersymmetry in the Green-Schwarz heterotic superstring☆

Abstract The computation of κ-anomalies in the Green-Schwarz heterotic superstring sigma-model and the corresponding Wess-Zumino consistency condition constitute a powerful alternative approach for the derivation of manifestly supersymmetric string effective actions. With respect to the beta-function approach this technique presents the advantage that a result which is obtained with the computation of beta-functions at n loops can be obtained through the calculation of κ-anomalies at n − 1 loops. In this paper we derive by a direct one-loop perturbative computation the κ-anomaly associated to the Yang-Mills Chern-Simons threeform, and, for the first time, the one associated to the Lorentz Chern-Simons threeform. In the calculation we shall use a convenient set of constraints for the pure N = 1, D = 10 supergravity theory which is algebraically identical to the standard set of constraints for the pure N = 1, D = 10 super Yang-Mills theory. Contrary to what is often stated in the literature we show that the Lorentz κ-anomaly gets contributions from the integration over both the fermionic and bosonic degrees of freedom of the string. A careful analysis of the absolute coefficients of all these anomalies reveals that they can be absorbed by setting dH = α′ 4 ( tr F 2 − tr R 2 ) , where α′ is the string tension, the expected result. We show that this relation ensures also the absence of gauge and Lorentz anomalies in the sigma-model effective action. Moreover, the consistency condition of the κ-anomalies ensures the closure of the SUSY algebra in the Bianchi identities. We exhibit the presence of infrared divergences in the heterotic string sigma model, which are due to the presence of the d = 2 scalar massless fields of the string, and present a conjecture for their cancellation which is intimately related to the locality and Wess-Zumino consistency of the κ-anomalies.