K-Theory and S-Duality: Starting Over from Square 3

TL;DR

This paper explores a new S-duality covariant extension of the spectral sequence in string theory, incorporating NS charged objects, and connects K-theory with M-theory through advanced mathematical and physical frameworks.

Contribution

It proposes a nonlinear, S-duality covariant extension of the Atiyah-Hirzebruch spectral sequence for classifying D-branes and NS objects, and relates it to M-theory.

Findings

Computed the MMS double-instanton contribution to d_5.

Proposed a conjecture for a nonlinear spectral sequence extension.

Connected K-theory classifications to M-theoretic structures.

Abstract

Recently Maldacena, Moore, and Seiberg (MMS) have proposed a physical interpretation of the Atiyah-Hirzebruch spectral sequence, which roughly computes the K-homology groups that classify D-branes. We note that in IIB string theory, this approach can be generalized to include NS charged objects and conjecture an S-duality covariant, nonlinear extension of the spectral sequence. We then compute the contribution of the MMS double-instanton configuration to the derivation d_5. We conclude with an M-theoretic generalization reminiscent of 11-dimensional E_8 gauge theory.