The finite and large-N behaviors of independent-value matrix models

Journal Article · Sat Mar 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4866316· OSTI ID:22251165

Ben Geloun, Joseph, E-mail: [e-mail] ^[1]; International Chair in Mathematical Physics and Applications, ICMPA–UNESCO Chair, 072 B.P. 50 Cotonou, Republic of Benin ^[2]; Klauder, John R., E-mail: [e-mail] ^[3]

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1. Perimeter Institute for Theoretical Physics, 31 Caroline St N, Waterloo, Ontario N2L 2Y5 (Canada)
2. (Benin)
3. Department of Physics and Department of Mathematics, University of Florida, Gainesville, Florida 32611-8440 (United States)

We investigate the finite and large N behaviors of independent-value O(N)-invariant matrix models. These are models defined with matrix-type fields and with no gradient term in their action. They are generically nonrenormalizable but can be handled by nonperturbative techniques. We find that the functional integral of any O(N) matrix trace invariant may be expressed in terms of an O(N)-invariant measure. Based on this result, we prove that, in the limit that all interaction coupling constants go to zero, any interacting theory is continuously connected to a pseudo-free theory. This theory differs radically from the familiar free theory consisting in putting the coupling constants to zero in the initial action. The proof is given for generic, finite-size matrix models, whereas, in the limiting case N → ∞, we succeed in showing this behavior for restricted types of actions using a particular scaling of the parameters.

• OSTI ID: 22251165
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COUPLING CONSTANTS
INTEGRALS
INTERACTIONS
MATRICES