Physics Group Meeting

We shall discuss the chiral algebras of a (0,2) sigma-model on homogeneous flag manifolds of various dimensions. As is by now well-known, the chiral algebras can be described by the theory of "Chiral Differential Operators" within perturbation theory. Beyond perturbation theory however, the picture changes radically; in the presence of worldsheet instantons, the chiral algebras will be completely trivialized. Consequently, supersymmetry is also spontaneously broken. A loop space analysis of the phenomenon leads us to a verification of a mathematical conjecture by Stolz concerning the scalar curvature of the loop spaces of such flag manifolds. Moreover, it also leads us to a new mathematical result about the kernel of certain twisted Dirac operators on these flag manifolds under a "quantum" deformation of their geometries.