$AdS_3$ backgrounds from 10D effective action of heterotic string theory

We present a method for calculating solutions and corresponding central charges for backgrounds with AdS{sub 3} and S{sup k} factors in {alpha}{sup '}-exact fashion from the full tree-level low-energy effective action of heterotic string theory. Three examples are explicitly presented: AdS{sub 3}xS{sup 3}xT{sup 4}, AdS{sub 3}xS{sup 2}xS{sup 1}xT{sup 4}, and AdS{sub 3}xS{sup 3}xS{sup 3}xS{sup 1}. Crucial property which enabled our analysis is vanishing of the Riemann tensor calculated from connection with ''{sigma}-model torsion.'' We show the following: (i) Chern-Simons terms are the only source of {alpha}{sup '} corrections not only in BPS, but also in non-BPS cases, suggesting a possible extension of general method of Kraus and Larsen, (ii) our results are in agreement with some conjectures on the form of the part of tree-level Lagrangian not connected to a mixed Chern-Simons term by supersymmetry (and present in all supersymmetric string theories), (iii) new {alpha}{sup '}-exact result for central charges in AdS{sub 3}xS{sup 3}xS{sup 3}xS{sup 1} geometry. As a tool we used our generalization of Sen's E-function formalism to AdS{sub p} with p>2, and paid special attention to proper definition of asymptotic charges.