On Orientifolds, Discrete Torsion, Branes and M Theory

TL;DR

The paper constructs a comprehensive M-theory framework for orientifold and orbifold planes by detailing the OMp lifts (OM2, OM5, OM1) and their charges, implementing discrete torsion via brane intersections and K-theory considerations, and elucidating SL(2,Z) duality as geometric on the M-theory torus. It systematically maps Type IIB orientifolds to their M lifts, derives new variants of O0 and orbifold lines, and extends the duality web to O5 and O1 cases, including novel brane intersection mechanisms that generate tension jumps. The work provides a unified picture connecting perturbative NSRR fluxes, nonperturbative M-theory effects, and dualities, and applies these insights to 4d N=4 spectra, BPS state structure, and the possibility of orientifold webs. Overall, it advances the understanding of nonperturbative orientifold dynamics, clarifies M-theory interpretations of discrete torsion, and proposes new variants with potential implications for gauge theories and dualities in string theory.

Abstract

We find some lifts to M theory of orientifold and orbifold planes including the O1, O3 and O5 planes of Type IIB and their transformations under SL(2,Z). The possible discrete torsion variants (or K theory classes) are explored, and are interpreted as arising from brane intersections with planes. We find new variants of the O0 and of an orbifold line (OF1) and determine their tensions in some cases. A systematic review of orientifolds, M orientifolds, and known M lifts, with some new clarifications is included together with a discussion of the role of T duality.