The Index Bundle for a Family of Dirac-Ramond Operators

2012/02/09 by Christopher L Harris, Harris, Chris
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1202.2049

openalex publication_date 2012/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the index bundle of the Dirac-Ramond operator associated with a family π: Z → X of compact spin manifolds. We view this operator as the formal twisted Dirac operator \dd ⊗ \bigotimes_n=1^∞S_qⁿTM_\C so that its index bundle is an element of K(X)[[q]]. When p₁ (Z) = 0, we derive some explicit formulas for the Chern character of this index bundle using its modular properties. We also use the modularity to identify our index bundle with an L(E₈) bundle in a special case.

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