Irreversibility of the Renormalization Group Flow in Two Dimensional Quantum Gravity

TL;DR

This paper demonstrates that the torus partition sum in two-dimensional (super) gravity decreases along the renormalization group flow, indicating irreversibility and a reduction in degrees of freedom over time.

Contribution

It establishes the monotonic decrease of the partition sum in 2D (super) gravity and explores implications for string theory and the space of models with central charge c ≤ 1.

Findings

Partition sum decreases with RG scale.

Confirms and extends Zamolodchikov's ideas.

Implications for degrees of freedom in string theory.

Abstract

We argue that the torus partition sum in $2d$ (super) gravity, which counts physical states in the theory, is a decreasing function of the renormalization group scale. As an application we chart the space of $(\hat c\leq1)$ $c\leq1$ models coupled to (super) gravity, confirming and extending ideas due to A. Zamolodchikov, and discuss briefly string theory, where our results imply that the number of degrees of freedom decreases with time.