Type II string theory and modularity

Abstract

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.

27 pages; clarifications added and typos corrected; to appear in JHEP

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Cited by in corpus (19)

• Non-conformality of gamma_i-deformed N=4 SYM theory
• What Does(n't) K-theory Classify?
• Duality symmetry and the form fields of M-theory
• Flux Quantization and the M-Theoretic Characters
• M-theory and Characteristic Classes
• M/F-Theory as Mf-Theory
• An approach to anomalies in M-theory via KSpin
• The Elliptic curves in gauge theory, string theory, and cohomology
• The character map in (twisted differential) non-abelian cohomology
• Twisted topological structures related to M-branes
• Ramond-Ramond fields and twisted differential K-theory
• A Higher Twist in String Theory
• Massey products in differential cohomology via stacks
• M-Theory with Framed Corners and Tertiary Index Invariants
• E8 Gauge Theory and Gerbes in String Theory
• Twisted K-Theory as a BRST Cohomology
• Flux Compactifications on Projective Spaces and The S-Duality Puzzle
• OP2 bundles in M-theory
• Some remarks on fundamental physical F-theory