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Non‐commutative field theories beyond perturbation theory
Author(s) -
Bietenholz W.,
Hofheinz F.,
Nishimura J.
Publication year - 2003
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200310092
Subject(s) - commutative property , field (mathematics) , theoretical physics , perturbation (astronomy) , mathematics , physics , pure mathematics , mathematical physics , quantum electrodynamics , quantum mechanics
We investigate two models in non‐commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally reduced matrix models. Using this technique, we measure Wilson loops in 2d NC gauge theory of rank 1. It turns out that they are non‐perturbatively renormalizable, and the phase follows an Aharonov‐Bohm effect if we identify θ = 1/ B . Next we study the 3d λ ϕ 4 model with two NC coordinates, where we present new results for the correlators and the dispersion relation. We further reveal the explicit phase diagram. The ordered regime splits into a uniform and a striped phase, as it was qualitatively conjectured before. We also confirm the recent observation by Ambjø rn and Catterall that such stripes occur even in d = 2, although they imply the spontaneous breaking of translation symmetry. However, in d = 3 and d = 2 we observe only patterns of two stripes to be stable in the range of parameters investigated.