Gauge Theories for Gravity on a Line

TL;DR

This paper discusses gauge theories for gravity formulated on a line, exploring their theoretical foundations and recent developments in two-dimensional models, with a tribute to Professor Polivanov's influence and contributions.

Contribution

It introduces a novel approach to gauge theories of gravity on a line, advancing understanding of two-dimensional gravitational models and their recent theoretical progress.

Findings

Summarizes recent developments in 2D gravity models

Proposes a new gauge-theoretic framework for gravity on a line

Connects the theory to Liouville models and quantum gravity

Abstract

Professor M. C. Polivanov and I met only a few times, during my infrequent visits to the-then Soviet Union in the 1970's and 1980's. His hospitality at the Moscow Steclov Institute made the trips a pleasure, while the scientific environment that he provided made them professionally valuable. But it is the human contact that I remember most vividly and shall now miss after his death. At a time when issues of conscience were both pressing for attention and difficult/dangerous to confront, Professor Polivanov made a deep impression with his quiet but adamant commitment to justice. I can only guess at the satisfaction he must have felt when his goal of gaining freedom for Yuri Orlov was attained, and even more so these days when human rights became defensible in his country; it is regrettable that he cannot now enjoy the future that he strived to attain. One of our joint interests was the Liouville theory,$^{1,\,2}$ which in turn can be viewed as a model for gravity in two-dimensional space-time. Some recent developments in this field are here summarized and dedicated to Polivanov's memory, with the hope that he would have enjoyed knowing about them.