2011/12/05 by Kevin J. Costello, Costello, Kevin J.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometry and complex manifolds #Quantum Algebra (math.QA) #math.AT #math.QA
paper · pdf · doi:10.48550/arxiv.1112.0816
91 pages. Version 2: typos corrected
openalex publication_date 2011/12/05 · arxiv created 2011/12/15 · arxiv updated 2011/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I give a rigorous construction of a 2-dimensional quantum field theory of maps from an elliptic curve to a compact complex manifold X, and I show that the partition function of this theory is the Witten genus of X. The results proved here were announced (in a slightly different form) in arXiv:1006.5422.