On subdivision invariant actions for random surfaces

TL;DR

This paper analyzes a subdivision invariant action for random surfaces, demonstrating its unphysical nature due to an infinite partition function, and suggests combining it with an area term for a viable theory.

Contribution

It critically evaluates a proposed subdivision invariant action and proposes a modification to achieve a physically meaningful model.

Findings

Partition function is infinite for all coupling constants

Subdivision invariant action is unphysical

Adding area action may stabilize the theory

Abstract

We consider a subdivision invariant action for dynamically triangulated random surfaces that was recently proposed (R.V. Ambartzumian et. al., Phys. Lett. B 275 (1992) 99) and show that it is unphysical: The grand canonical partition function is infinite for all values of the coupling constants. We conjecture that adding the area action to the action of Ambartzumian et. al. leads to a well-behaved theory.