On the relation between non-commutative field theories at theta = infinity and large N matrix field theories

Abstract

It is well-known that non-commutative (NC) field theories at theta = infinity are ``equivalent'' to large N matrix field theories to all orders in perturbation theory, due to the dominance of planar diagrams. By formulating a NC field theory on the lattice non-perturbatively and mapping it onto a twisted reduced model, we point out that the above equivalence does not hold if the translational symmetry of the NC field theory is broken spontaneously. As an example we discuss NC scalar field theory, where such a spontaneous symmetry breakdown has been confirmed by Monte Carlo simulations.

12 pages, LaTeX

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• Lectures on Matrix Field Theory I
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion
• Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study
• Matrix Model Fixed Point of Noncommutative Phi-Four
• The instability of intersecting fuzzy spheres
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Dynamical generation of mass in the noncommutative supersymmetric Schwinger model
• Wilson RG of Noncommutative ${\Phi }_4^4$