Heterotic non-linear sigma models with anti-de Sitter target spaces

We calculate the beta function of non-linear sigma models with S^{D + 1} and AdS_{D + 1} target spaces in a 1 / D expansion up to order 1 / D² and to all orders in α^′. This beta function encodes partial information about the spacetime effective action for the heterotic string to all orders in α^′. We argue that a zero of the beta function, corresponding to a worldsheet CFT with AdS_{D + 1} target space, arises from competition between the one-loop and higher-loop terms, similarly to the bosonic and supersymmetric cases studied previously in [J.J. Friess, S.S. Gubser, Non-linear sigma models with anti-de Sitter target spaces, Nucl. Phys. B 750 (2006) 111-141]. Various critical exponents of the non-linear sigma model are calculated, and checks of the calculation are presented.