1993/12/13 by Edward Witten, Witten, Edward · 1 voice · 235 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Computer science #Equivariant cohomology #FOS: Mathematics #FOS: Physical sciences #Grassmannian #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Linguistics #Mathematics #Path (computing) #Philosophy #Physics #Pure mathematics #Quantum #Quantum Algebra (math.QA) #Quantum cohomology #Quantum mechanics #Space (punctuation) #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.hep-th/9312104
published in arXiv (Cornell University) (Cornell University) · 78 pages
arxiv created 1993/12/13 · openalex publication_date 1993/12/13 · arxiv published 1993/12/13 · arxiv updated 1993/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
The article is devoted to a quantum field theory explanation of the relationship (noticed some years ago by Gepner) between the Verlinde algebra of the group U(k) at level N-k and the cohomology of the Grassmannian. The argument proceeds by starting with the two dimensional sigma model whose target space is the Grassmannian and integrating out some fields in a standard way. It has long been known that the resulting low energy effective action describes a theory with a mass gap; the novelty here is that this theory in fact is equivalent at long distances to a gauged WZW model of U(k)/U(k), and hence is related to the Verlinde algebra.