Phase space distribution of Riemann zeros

Abstract

We present the partition function of a most generic U(N) single plaquette model in terms of representations of a unitary group. Extremising the partition function in a large N limit, we obtain a relation between eigenvalues of unitary matrices and the number of boxes in the most dominant Young tableaux distribution. Since the eigenvalues of unitary matrices behave like coordinates of free fermions, whereas the number of boxes in a row is like conjugate momenta of the same, a relation between them allows us to provide a phase space distribution for different phases of the unitary model under consideration. This proves a universal feature that all the phases of a generic unitary matrix model can be described in terms of topology of free fermi phase space distribution. Finally, using this result and analytic properties of resolvent that satisfy the Dyson-Schwinger equation, we present a phase space distribution of unfolded zeros of the Riemann zeta function.