The Master Field for Large $N$ Matrix Models and Quantum Groups

Details The Master Field for Large $N$ Matrix Models and Quantum Groups The Master Field for Large $N$ Matrix Models and Quantum Groups

1995-03-07

arxiv.org/abs/hep-th/9503041v1

Mod.Phys.Lett. A10 (1995) 2323-2334

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTex

Scientific paper

10.1142/S0217732395002489

In recent works by Singer, Douglas and Gopakumar and Gross an application of results of Voiculescu from non-commutative probability theory to constructions of the master field for large $N$ matrix field theories have been suggested. In this note we consider interrelations between the master field and quantum groups. We define the master field algebra and observe that it is isomorphic to the algebra of functions on the quantum group $SU_q(2)$ for $q=0$. The master field becomes a central element of the quantum group Hopf algebra. The quantum Haar measure on the $SU_q(2)$ for any $q$ gives the Wigner semicircle distribution for the master field. Coherent states on $SU_q(2)$ become coherent states in the master field theory.

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