On The DouglasKazakov Phase Transition
Abstract
We give a rigorous proof of the fact that a phase transition discovered by Douglas and Kazakov in 1993 in the context of twodimensional gauge theories occurs. This phase transition can be formulated in terms of the Brownian bridge on the unitary group U(N) when N tends to infinity. We explain how it can be understood by considering the asymptotic behaviour of the eigenvalues of the unitary Brownian bridge, and how it can be technically approached by means of Fourier analysis on the unitary group. Moreover, we advertise some more or less classical methods for solving certain minimisation problems which play a fundamental role in the study of the phase transition.
 Publication:

arXiv eprints
 Pub Date:
 March 2015
 DOI:
 10.48550/arXiv.1503.00502
 arXiv:
 arXiv:1503.00502
 Bibcode:
 2015arXiv150300502L
 Keywords:

 Mathematics  Probability;
 Mathematical Physics