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Triangle-hinge models [arXiv:1503.08812] are introduced to describeworldvolume dynamics of membranes. The Feynman diagrams consist of trianglesglued together along hinges and can be restricted to tetrahedral decompositionsin a large N limit. In this paper, after clarifying that all the tetrahedraresulting in the original models are orientable, we define a version oftriangle-hinge models that can describe the dynamics of unoriented membranes.By regarding each triangle as representing a propagation of an open membrane ofdisk topology, we introduce a local worldvolume parity transformation whichinverts the orientation of triangle, and define unoriented triangle-hingemodels by gauging the transformation. Unlike two-dimensional cases, this localtransformation generally relates a manifold to a nonmanifold, but still is awell-defined manipulation among tetrahedral decompositions. We further showthat matter fields can be introduced in the same way as in the originaloriented models. In particular, the models will describe unoriented membranesin a target spacetime by taking matter fields to be the target spacecoordinates.

Triangle-hinge models for unoriented membranes