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

We calculate the beta function of non-linear sigma models with SD+1 and AdSD+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 AdSD+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.