From Virasoro Algebra to Cosmology

TL;DR

This paper explores how the Virasoro algebra's coadjoint representation relates to four-dimensional cosmology, highlighting the role of the diffeomorphism field and projective geometry in connecting string theory concepts to cosmological models.

Contribution

It introduces a novel connection between the Virasoro algebra, projective geometry, and cosmology through the diffeomorphism field and the Thomas-Whitehead gravitational action.

Findings

Link between Virasoro algebra and cosmological models

Role of the diffeomorphism field in higher-dimensional gravity

Mathematical framework connecting projective geometry to cosmology

Abstract

Earlier work of Balachandran and friends provided a map from algebras to field theories. These methods provide insight into quantum gauge theories and anomalies. In this note we take the reader from the coadjoint representation of the Virasoro algebra to four- (and higher-) dimensional gravitation and cosmology. The protagonist in this story is a component of the projective connection, the diffeomorphism field, which straddles between the one-dimensional world of initial data in string theories to cosmology in four dimensions. We review mathematical intuition that ties projective geometry to the Virasoro algebra, the Thomas\textendash Whitehead (TW) gravitational action that gives the diffeomorphism field dynamics and the building blocks for gauge projective Dirac action.