The Chiral de Rham Complex and Positivity of the Equivariant Signature   of the Loop Space
  In this note we show that the positivity property of the equivariant signature of the loop space, first observed in [MS1] in the case of the even-dimensional projective spaces, is valid for   Picard number 2 toric varieties. A new formula for the equivariant signature of the loop space in the case of a toric spin variety is derived. 
V. Gorbounov (University of Kentucky, USA), F. Malikov (University of   Southern California, USA)