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• W3100940031 abstract "We study quartic matrix models with partition function Z[E,J]=int dM exp(trace(JM-EM^2-(lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, lambda>0 is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing beta-function. As main application we prove that Euclidean phi^4-quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for N->infty the same spectrum as the Laplace operator in 4 dimensions. Using the theory of singular integral equations of Carleman type we compute (for N->infty and after renormalisation of E,lambda) the free energy density (1/volume)log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which we verified numerically for coupling constants 0<lambdaleq (1/pi)." @default.
• W3100940031 created "2020-11-23" @default.
• W3100940031 creator A5028961771 @default.
• W3100940031 creator A5066470660 @default.
• W3100940031 date "2014-03-29" @default.
• W3100940031 modified "2023-09-26" @default.
• W3100940031 title "Self-Dual Noncommutative $${phi^4}$$ ϕ 4 -Theory in Four Dimensions is a Non-Perturbatively Solvable and Non-Trivial Quantum Field Theory" @default.
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• W3100940031 doi "https://doi.org/10.1007/s00220-014-1906-3" @default.
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