2005/01/31 by Igor Kriz, Igor Kříž, Hisham Sati
Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Cohomology #Compactification (mathematics) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Mirror symmetry #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #String theory #Theoretical physics #hep-th #math.AT
paper · pdf · doi:10.1088/1126-6708/2005/08/038
published as JHEP 0508 (2005) 038 · 27 pages; clarifications added and typos corrected; to appear in JHEP
arxiv created 2005/07/31 · openalex publication_date 2005/08/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper, in a sense, completes a series of three papers. In the previous two hep-th/0404013, hep-th/0410293, we have explored the possibility of refining the K-theory partition function in type II string theories using elliptic cohomology. In the present paper, we make that more concrete by defining a fully quantized free field theory based on elliptic cohomology of 10-dimensional spacetime. Moreover, we describe a concrete scenario how this is related to compactification of F-theory on an elliptic curve leading to IIA and IIB theories. We propose an interpretation of the elliptic curve in the context of elliptic cohomology. We discuss the possibility of orbifolding of the elliptic curves and derive certain properties of F-theory. We propose a link of this to type IIB modularity, the structure of the topological Lagrangian of M-theory, and Witten's index of loop space Dirac operators.