The cancellation of worldsheet anomalies in the D=10 Green--Schwarz   heterotic string sigma--model
  We determine the two--dimensional Weyl, Lorentz and $\kappa$--anomalies in the $D=10$ Green--Schwarz heterotic string sigma--model, in an $SO(1,9)$-Lorentz covariant background gauge, and prove their cancellation. 
K. Lechner and M. Tonin