Riemann Hypothesis, Matrix/Gravity Correspondence and FZZT Brane Partition Functions

We investigate the physical interpretation of the Riemann zeta function as a FZZT brane partition function associated with a matrix/gravity correspondence. The Hilbert-Polya operator in this interpretation is the master matrix of the large N matrix model. Using a related function Ξ(z) we develop an analog between this function and the Airy function Ai(z) of the Gaussian matrix model. The analogy gives an intuitive physical reason why the zeros lie on a critical line. Using a Fourier transform of the Ξ(z) function we identify a Kontsevich integrand. Generalizing this integrand to n×n matrices we develop a Kontsevich matrix model which describes n FZZT branes. The Kontsevich model associated with the Ξ(z) function is given by a superposition of Liouville type matrix models that have been used to describe matrix model instantons.