Induced quantum gravity on a Riemann Surface

TL;DR

This paper explores induced quantum gravity on Riemann surfaces across various dimensions, demonstrating preservation of classical W-symmetry during quantization and revealing quantum-induced modifications to target coordinates.

Contribution

It introduces a simple model for quantum gravity on Riemann surfaces, showing how quantum corrections affect target space coordinates while maintaining classical symmetries.

Findings

W-symmetry preserved on-shell at all orders

Quantum corrections induce non-trivial target coordinate behavior

Model successfully quantized perturbatively

Abstract

Induced quantum gravity dynamics built over a Riemann surface is studied in arbitrary dimension. Local coordinates on the target space are given by means of the Laguerre-Forsyth construction. A simple model is proposed and pertubatively quantized. In doing so, the classical W-symmetry turns out to be preserved on-shell at any order of the $\hbar$ perturbative expansion. As a main result, due to quantum corrections, the target coordinates acquire a non-trivial character.