$O(d,d)$ Symmetry in Quantum Cosmology

TL;DR

This paper studies quantum cosmology models with $O(d,d)$ symmetry, solving the Wheeler--de Witt equation explicitly and constructing wave functions with well-defined symmetry properties, including applications to 2D black holes.

Contribution

It provides explicit solutions to the Wheeler--de Witt equation in $O(d,d)$ symmetric models and explores their transformation properties, including scale factor duality.

Findings

Explicit solutions to Wheeler--de Witt equation with $O(d,d)$ symmetry.

Wave functions with well-defined transformation properties.

Application to 2D black hole models.

Abstract

We analyze the quantum cosmology of one--loop string effective models which exhibit an $O(d,d)$ symmetry. It is shown that due to the large symmetry of these models the Wheeler--de Witt equation can completely be solved. As a result, we find a basis of solutions with well defined transformation properties under $O(d,d)$ and under scale factor duality in particular. The general results are explicitly applied to 2--dimensional target spaces while some aspects of higher dimensional cases are also discussed. Moreover, a semiclassical wave function for the 2-dimensional black hole is constructed as a superposition of our basis.