Vanishing Chiral Algebras and Höhn-Stolz Conjecture

2010/02/01 by Junya Yagi, Yagi, Junya
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #hep-th #math.AT #math.DG

paper · pdf · doi:10.48550/arxiv.1002.0028

8 pages. v2: Major revision. To appear in the proceedings of String-Math 2011 conference

openalex publication_date 2010/02/01 · arxiv created 2012/07/21 · arxiv updated 2012/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a two-dimensional quantum field theory with (0,2) supersymmetry, one can construct a chiral (or vertex) algebra. The chiral algebra of a (0,2) supersymmetric sigma model is, perturbatively, the cohomology of a sheaf of chiral differential operators on a string Kähler manifold. However, it vanishes in some cases when instantons are taken into account. I will discuss the implication of this phenomenon for the Höhn-Stolz conjecture on the Witten genus.

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