Large representation recurrences in large N random unitary matrix models

Joanna L. Karczmarek, Gordon W. Semenoff
2011 Journal of High Energy Physics  
In a random unitary matrix model at large N, we study the properties of the expectation value of the character of the unitary matrix in the rank k symmetric tensor representation. We address the problem of whether the standard semiclassical technique for solving the model in the large N limit can be applied when the representation is very large, with k of order N. We find that the eigenvalues do indeed localize on an extremum of the effective potential; however, for finite but sufficiently
more » ... k/N, it is not possible to replace the discrete eigenvalue density with a continuous one. Nonetheless, the expectation value of the character has a well-defined large N limit, and when the discreteness of the eigenvalues is properly accounted for, it shows an intriguing approximate periodicity as a function of k/N.
doi:10.1007/jhep10(2011)066 fatcat:6wel5bv24bepxc5smn35imcfne