PT symmetry and large-N models

Details PT symmetry and large-N models PT symmetry and large-N models

2008-04-04

arxiv.org/abs/0804.0778v1

J.Phys.A41:244021,2008

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, to be published in J. Phys. A special issue on Pseudo Hermitian Hamiltonians in Quantum Physics

Scientific paper

10.1088/1751-8113/41/24/244021

Recently developed methods for PT-symmetric models can be applied to quantum-mechanical matrix and vector models. In matrix models, the calculation of all singlet wave functions can be reduced to the solution a one-dimensional PT-symmetric model. The large-N limit of a wide class of matrix models exists, and properties of the lowest-lying singlet state can be computed using WKB. For models with cubic and quartic interactions, the ground state energy appears to show rapid convergence to the large-N limit. For the special case of a quartic model, we find explicitly an isospectral Hermitian matrix model. The Hermitian form for a vector model with O(N) symmetry can also be found, and shows many unusual features. The effective potential obtained in the large-N limit of the Hermitian form is shown to be identical to the form obtained from the original PT-symmetric model using familiar constraint field methods. The analogous constraint field prescription in four dimensions suggests that PT-symmetric scalar field theories are asymptotically free.

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