Consistency Conditions for Fivebrane in M Theory on R^5/Z_2 Orbifold

TL;DR

The paper derives general consistency conditions for M-theory fivebranes on ${f R}^5/{f Z}_2$ via flux quantization, showing local obstructions to t-configurations and odd intersections with the ${f Z}_2$ fixed plane, and uses these to formulate reliable brane constructions. It then realizes orientifold four-planes within M-theory, distinguishing $SO$- and $Sp$-types through RR holonomy and RR U(1) data, and analyzes their T-duality to O5-planes. By applying these insights to brane configurations, the work models ${f N}=2$ SQCD with symplectic and orthogonal gauge groups, resolves inconsistencies in earlier proposals, and derives brane-creation and s-rule phenomena in orientifold backgrounds. The results provide a nonperturbative, M-theory-based framework for orientifold planes and brane dynamics in singular geometries, with connections to Seiberg-Witten curves and Higgs-branch structures.

Abstract

We derive some consistency conditions for fivebrane in M theory on R^5/Z_2 orbifold from the quantization law for the antisymmetric tensor field. We construct consistent fivebrane configurations in R^5/Z_2 type orbifold that exhibit the correct low energy dynamics of N=2 SQCD in four dimensions with symplectic and orthogonal gauge groups. This leads us to propose the M theory realization of orientifold four-planes of various types, and we study their properties by applying the consistency conditions.

Figures (9)

• Figure 1: The Corrected Curve (a Generic Point of the Coulomb Branch)
• Figure 2: Creation of Fivebrane
• Figure 3: D6-brane Dividing O4-plane
• Figure 4: The Question
• Figure 5: The Answer