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Supersymmetry and the Atiyah-Singer index theorem
Using a recently introduced index for supersymmetric theories, we present a simple derivation of the Atiyah-Singer index theorem for classical complexes and itsG-index generalization using elementary
Theta functions, modular invariance, and strings
We use Quillen's theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory. In particular, we show that the spin structure
Potentials for the supersymmetric nonlinear σ-model
The most general structure for potential terms compatible withN=1,N=2, andN=4 supersymmetry in the nonlinear σ-model in two space-time dimensions is determined. The differential geometry of the
Bosonization on higher genus Riemann surfaces
We prove the equivalence between certain fermionic and bosonic theories in two spacetime dimensions. The theories have fields of arbitrary spin on compact surfaces with any number of handles. Global