Nonperturbative evaluation of the partition function for the real scalar quartic QFT on the Moyal plane at weak coupling
arXiv:1809.09453 · doi:10.1063/1.5063293
Abstract
The remarkable properties of the real scalar quartic quantum field theory on the Moyal plane in combination with its similarity to the Kontsevich model make the model's partition function an interesting object to study. However, direct evalua- tions is obstructed by the intertwining of the field's various modes. A factorization procedure to circumvent this problem is proposed and discussed here in the context of the real scalar quartic qft on the Moyal plane. This factorization consists of integrating against the asymptotic volume of the diagonal subpolytope of symmet- ric stochastic matrices. This volume has been determined to this end. Using this method the partition function for regime of weak coupling is computed. Using the same method it is as well possible to determine the partition function and free energy density for other regimes.
References in corpus (16)
- 2D Gravity and Random Matrices
- Noncommutative Perturbative Dynamics
- Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
- Algebras of distributions suitable for phase-space quantum mechanics. I
- Duality in Scalar Field Theory on Noncommutative Phase Spaces
- Renormalisation of ϕ^4-theory on noncommutative R^2 in the matrix base
- Vanishing of Beta Function of Non Commutative Theory to all orders
- Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
- Power-counting theorem for non-local matrix models and renormalisation
- On some integrals over the U(N) unitary group and their large N limit
- Renormalisation of ϕ^4-theory on noncommutative R^4 to all orders
- Self-dual noncommutative ϕ^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
- Renormalization of the noncommutative phi^3 model through the Kontsevich model
- A nontrivial solvable noncommutative ϕ^3 model in 4 dimensions
- The asymptotic volume of diagonal subpolytopes of symmetric stochastic matrices
- Partition function methods for the quartic scalar quantum field theory on the Moyal plane