Three dimensional field theories from infinite dimensional lie algebras

TL;DR

This paper introduces a method to construct three-dimensional topological field theories from infinite-dimensional Lie algebras, revealing new connections to gravity and extensions to W_3-gravity.

Contribution

It presents a novel procedure for deriving 3D topological actions from centrally extended Lie groups, including the Virasoro and W_3 algebras, linking them to gravity theories.

Findings

Constructed 3D Chern-Simons theories from Kac-Moody and Virasoro groups.

Identified a new 3D topological field theory related to Virasoro algebra.

Connected the theory to two-dimensional induced gravity in the chiral gauge.

Abstract

A procedure for constructing topological actions from centrally extended Lie groups is introduced. For a \km\ group, this produces \3al \cs, while for the \vir\ group the result is a new \3al \tft\ whose physical states satisfy the \vir\ \wi. This \tft\ is shown to be a first order formulation of two dimensional induced gravity in the chiral gauge. The extension to $W_3$-gravity is discussed.