Elliptic genera and quantum field theory

It is shown that in elliptic cohomology - as recently formulated in the mathematical literature - the supercharge of the supersymmetric nonlinear signa model plays a role similar to the role of the Dirac operator in K-theory. This leads to several insights concerning both elliptic cohomology and string theory. Some of the relevant calculations have been done previously by Schellekens and Warner in a different context.