Duality constructions from quantum state manifolds

Date
2015-11-20
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS2/CF T1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.
Description
CITATION: Kriel, J. N., Van Zyl, H. J. R. & Scholtz, F. G. 2015. Duality constructions from quantum state manifolds. Journal of High Energy Physics, 140, doi:10.1007/JHEP11(2015)14.
The original publication is available at http://link.springer.com/journal/13130
Keywords
Holography, 2D Gravity, Geometrical constructions, Geometric quantization, Geometry, Differential, Manifolds (Mathematics), Symmetry (Mathematics), Condensed matter
Citation
Kriel, J. N., Van Zyl, H. J. R. & Scholtz, F. G. 2015. Duality constructions from quantum state manifolds. Journal of High Energy Physics, 140, doi:10.1007/JHEP11(2015)14.