A non-perturbative study of non-commutative U(1) gauge theory

Understand

We study U(1) gauge theory on a 4d non-commutative torus, where two directions are non-commutative.

• Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2.
• At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance.
• In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter theta, which provides evidence for a possible continuum theory.