Nonperturbative evaluation of the partition function for the real scalar quartic QFT on the Moyal plane at weak coupling

Abstract

The remarkable properties of the real scalar quartic quantum field theory on the Moyal plane in combination with its similarities to the Kontsevich model make the model’s partition function an interesting object to study. However, the intertwinement of the eigenvalues of the external matrix prevents a direct evaluation. In this paper, we develop a factorization procedure to circumvent this problem and discuss it in the context of the real scalar quartic quantum field theory on the Moyal plane. The factorization consists of integration against the asymptotic volume of the diagonal subpolytope of symmetric stochastic matrices. The partition function in the weak coupling regime can be computed in this way. This method should also extend to other regimes.