Quantization of the First-Order Two-Dimensional Einstein-Hilbert Action

TL;DR

This paper performs a canonical analysis and quantization of the 2D Einstein-Hilbert action, revealing its gauge symmetry, absence of physical degrees of freedom, and that higher-loop diagrams vanish, with one-loop contributions canceling out.

Contribution

It introduces a novel gauge symmetry in the 2D Einstein-Hilbert action and demonstrates the vanishing of all loop diagrams beyond one-loop order.

Findings

All loop diagrams beyond one-loop vanish.

One-loop two-point function cancels due to ghost and graviton contributions.

The action has no physical degrees of freedom and exhibits an unusual gauge symmetry.

Abstract

A canonical analysis of the first-order two-dimensional Einstein-Hilbert action has shown it to have no physical degrees of freedom and to possess an unusual gauge symmetry with a symmetric field $\xi_{\mu\nu}$ acting as a gauge function. Some consequences of this symmetry are explored. The action is quantized and it is shown that all loop diagrams beyond one-loop order vanish. Furthermore, explicit calculation of the one-loop two-point function shows that it too vanishes, with the contribution of the ghost loop cancelling that of the ``graviton'' loop.