Type IIB String Theory, S-Duality, and Generalized Cohomology

TL;DR

This paper explores the limitations of twisted K-theory in describing type IIB string theory with S-duality and proposes elliptic cohomology as a promising alternative, also proving a relevant conjecture of Witten.

Contribution

It introduces elliptic cohomology as a new framework for type IIB string theory, addressing S-duality issues unresolvable by twisted K-theory, and proves Witten's conjecture on spin cobordism.

Findings

Twisted K-theory cannot fully capture S-duality in type IIB string theory.

Elliptic cohomology offers a potential resolution to this problem.

Proved Witten's conjecture that the 11-dimensional spin cobordism group vanishes on K(Z,6).

Abstract

In the presence of background Neveu-Schwarz flux, the description of the Ramond-Ramond fields of type IIB string theory using twisted K-theory is not compatible with S-duality. We argue that other possible variants of twisted K-theory would still not resolve this issue. We propose instead a possible path to a solution using elliptic cohomology. We also discuss T-duality relation of this to a previous proposal for IIA theory, and higher-dimensional limits. In the process, we obtain some other results which may be interesting on their own. In particular, we prove a conjecture of Witten that the 11-dimensional spin cobordism group vanishes on K(Z,6), which eliminates a potential new theta-angle in type IIB string theory.