Exactly Marginal Operators and Running Coupling Constants in 2D Gravity

TL;DR

This paper investigates new terms in the Liouville action for 2D quantum gravity coupled to matter, showing they ensure the exact marginality of interactions and influence the renormalization group flow, with implications for matrix model results.

Contribution

It introduces previously overlooked terms in the Liouville action that guarantee the exact marginality of dressed interactions in 2D gravity coupled to matter.

Findings

New terms are crucial for the renormalization group flow.

Terms are observed up to second order in coupling.

Results align with recent matrix model phase diagrams.

Abstract

The Liouville action for two--dimensional quantum gravity coupled to interacting matter contains terms that have not been considered previously. They are crucial for understanding the renormalization group flow and can be observed in recent matrix model results for the phase diagram of the Sine--Gordon model coupled to gravity. These terms insure, order by order in the coupling constant, that the dressed interaction is exactly marginal. They are discussed up to second order.