Chiral Algebras of (0,2) Sigma Models: Beyond Perturbation Theory - II

TL;DR

This paper demonstrates that worldsheet instantons trivialize the chiral algebras of (0,2) sigma models on complete flag manifolds, leading to spontaneous supersymmetry breaking and supporting Stolz's conjecture about harmonic spinors.

Contribution

It extends previous work to show that instantons cause total trivialization of chiral algebras in (0,2) sigma models on all complete flag manifolds, revealing new insights into supersymmetry breaking.

Findings

Chiral algebras are trivialized by instantons on all complete flag manifolds.

Supersymmetry is spontaneously broken in these models.

Supports Stolz's conjecture regarding harmonic spinors on loop spaces.

Abstract

We extend our analysis in [arXiv:0801.4782] and show that the chiral algebras of (0,2) sigma models are totally trivialized by worldsheet instantons for all complete flag manifolds of compact semisimple Lie groups. Consequently, supersymmetry is spontaneously broken. Our results verify Stolz's idea that there are no harmonic spinors on the loop spaces of these flag manifolds. Moreover, they also imply that the kernels of certain twisted Dirac operators on these spaces will be empty under a "quantum" deformation of their geometries.