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

TL;DR

This paper investigates the non-perturbative relationship between non-commutative field theories at infinite theta and large N matrix theories, highlighting the breakdown of equivalence due to spontaneous symmetry breaking.

Contribution

It demonstrates that the known perturbative equivalence between NC field theories at theta = infinity and large N matrix theories does not extend non-perturbatively when translational symmetry is spontaneously broken.

Findings

Spontaneous symmetry breaking occurs in NC scalar field theory.

The non-perturbative equivalence fails in the broken symmetry phase.

Monte Carlo simulations confirm the symmetry breakdown.

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.