On Induced Gravity in 2-d Topological Theories

TL;DR

This paper investigates how gravity can emerge in two-dimensional topological gauge theories by analyzing wave functionals and the induced metrics across different gauge representations.

Contribution

It provides a quantum-level analysis of induced gravity in 2D $\,\, ext{ extphi}F$ gauge theories, highlighting the role of gauge representations in metric emergence.

Findings

Singlet representation corresponds to a topological universe.

Non-singlet representations induce a residual gauge-invariant metric.

The induced metric is rigid, inherited from the group metric.

Abstract

We study 2-d $\phi F$ gauge theories with the objective to understand, also at the quantum level, the emergence of induced gravity. The wave functionals - representing the eigenstates of a vanishing flat potential - are obtained in the $\phi$ representation. The composition of the space they describe is then analyzed: the state corresponding to the singlet representation of the gauge group describes a topological universe. For other representations a metric which is invariant under the residual gauge group is induced, apart from possible topological obstructions. Being inherited from the group metric it is rather rigid.