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

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.

16 pages, latex, no figures. No changes at all. Replaced due to a .ps file problem

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• Cosmological solutions, p-branes and the Wheeler-DeWitt equation
• Expanding and contracting universes in third quantized string cosmology
• Supersymmetric Quantization of Anisotropic Scalar-Tensor Cosmologies
• String cosmology versus standard and inflationary cosmology
• Low-energy quantum string cosmology
• Equations of Motion in Double Field Theory: From Particles to Scale Factors
• Duality transformation and conformal equivalent scalar-tensor theories
• Modular Quantum Cosmology
• Non-linearities in the quantum multiverse
• Quantum Cosmology in $f(Q)$ theory
• $O(d,d)$ symmetry in teleparallel dark energy