Quotient of a loop group and Witten genus

摘要

We define a Dirac-Ramond operator over the quotient (LG)/H of a loop group by a subgroup H of the compact Lie group G. We state the conjecture that its equivariant Index with respect of the natural circle action over the quotient of the loop group is equal to the Witten genus of the homogeneous manifold G/H. We motivate the conjecture by a short time argument which allows to come back to a Dirac-Ramond operator at the manner of Taubes on a limit model where all the computations can be done by hand. (C) 2001 American Institute of Physics. [References: 36]