The antibracket (or Poisson-bracket) in a 2-dim sigma-model induces a generalized Schouten-bracket for totally antisymmetric (or totally symmetric) generalized multivector fields. The integrability of a generalized almost complex structure J is equivalent to the vanishing of this bracket of J with itself. The master equation for Zucchini’s Hitchin-sigma-model can thus be redarded as the integrability condition for J.

TU, Vienna and SPhT/Saclay