Type II string theory and modularity

TL;DR

This paper develops a fully quantized elliptic cohomology-based field theory for type II string theories, linking it to F-theory compactification, modularity, and topological invariants.

Contribution

It introduces a concrete elliptic cohomology framework for type II string theories and relates it to F-theory, modularity, and topological aspects of M-theory.

Findings

Defined a quantized elliptic cohomology field theory for 10D spacetime

Connected elliptic cohomology to F-theory compactification scenarios

Explored implications for type IIB modularity and topological invariants

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.