To understand the simple form of the action , recall that the curvature term in Regge calculus (cf. 12) is represented by , which for fixed edge length is proportional to . The constant is determined from the condition that a triangulation of flat space should have average vanishing curvature [2, 11]. (Because the four-simplices are equilateral, zero curvature can only be achieved upon averaging. This explains the absence of a conventional perturbation theory around flat space.) The cosmological term is represented by . It is sometimes convenient to re-express as a function of , using , valid for the -topology. The corresponding partition function is (where ).
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