Triangle-hinge models for unoriented membranes

Understand

Triangle-hinge models [arXiv:1503.08812] are introduced to describe worldvolume dynamics of membranes.

• The Feynman diagrams consist of triangles glued together along hinges and can be restricted to tetrahedral decompositions in a large N limit.
• In this paper, after clarifying that all the tetrahedra resulting in the original models are orientable, we define a version of triangle-hinge models that can describe the dynamics of unoriented membranes.
• By regarding each triangle as representing a propagation of an open membrane of disk topology, we introduce a local worldvolume parity transformation which inverts the orientation of triangle, and define unoriented triangle-hinge models by gauging the transformation.