Instantonic Branes, Atiyah-Hirzebruch Spectral Sequence, and SL(2,Z) duality of N=4 SYM

TL;DR

This paper explores the mathematical classification of orientifold three-planes using the Atiyah-Hirzebruch Spectral Sequence and relates these classifications to SL(2,Z) duality in four-dimensional N=4 super Yang-Mills theories.

Contribution

It extends the spectral sequence to include NS-NS fluxes and links the mathematical equivalences to physical SL(2,Z) duality in N=4 SYM.

Findings

Mathematical classification of orientifold planes via spectral sequence

Extension of the sequence to include NS-NS fluxes

Interpretation of equivalences as SL(2,Z) duality in N=4 SYM

Abstract

We study the equivalence among orientifold three-planes in the context of the Atiyah-Hirzebruch Spectral Sequence. This equivalence refers to the fact that two different cohomology classes in the same cohomology group, which classify the orientifolds, are lifted to the same trivial class in K-theory. The physical interpretation of this mathematical algorithm is given by the role of D-brane instantons. By following some recent ideas, we extend the sequence to include a classification of NS-NS fluxes. We find that such equivalences, in the low energy limit of the dynamics on the worldvolume of type IIB D3-branes on top of the orientifolds, are interpreted as the SL(2,Z) duality in four dimensional N=4 SYM theories.