
Triangle–hinge models for unoriented membranesTriangle–hinge models for unoriented membranes 
"/Fukuma, Masafumi/"Fukuma, Masafumi ,
"/Sugishita, Sotaro/"Sugishita, Sotaro ,
"/Umeda, Naoya/"Umeda, Naoya
2016
(
7
)
20160712 , Oxford University Press (OUP)
ISSN:20503911
Description
Triangle–hinge models [M. Fukuma, S. Sugishita, and N. Umeda, J. High Energy Phys. 1507, 088 (2015)] 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 largeNN 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 a triangle, and define unoriented triangle–hinge models by gauging the transformation. Unlike twodimensional cases, this local transformation generally relates a manifold to a nonmanifold, but still is a welldefined manipulation among tetrahedral decompositions. We further show that matter fields can be introduced in the same way as in the original oriented models. In particular, the models will describe unoriented membranes in a target spacetime by taking matter fields to be the target space coordinates.
FullText
http://repository.kulib.kyotou.ac.jp/dspace/bitstream/2433/216698/1/ptep_ptw069.pdf