Exact Solution of 2D Poincare Gravity Coupled to Fermion Matter

TL;DR

This paper provides an exact classical solution for a two-dimensional gravity model coupled with massless Dirac fermions, specifically in the case of chiral fermions, advancing understanding of 2D quantum gravity.

Contribution

It presents the first exact integration of the classical equations of motion for 2D Poincare gravity coupled to chiral fermion matter.

Findings

Exact solutions for 2D gravity with chiral fermions

Demonstrates integrability of the model's equations of motion

Provides a foundation for further quantum analysis

Abstract

The 2D model of gravity with zweibeins $e^{a}$ and the Lorentz connection one-form $\omega^{a}_{\ b}$ as independent gravitational variables coupled to 2d massless Dirac matter is considered. It is shown that the classical equations of motion are exactly integrated in the case of chiral fermions.