Twisted Eguchi-Kawai Reduced Chiral Models

We study the twisted Eguchi-Kawai (TEK) reduction procedure for large N unitary matrix lattice models. In particular, we consider the case of twodimensional principal chiral models, and use numerical Monte Carlo (MC) simulations to check the conjectured equivalence of TEK reduced model and standard lattice model in the large-N limit. The MC results are compared with the large-N limit of lattice principal chiral models to verify the supposed equivalence. The consistency of the TEK reduction procedure is verified in the strong-coupling region, i.e. for β < βc where βc is the location of the large-N phase transition. On the other hand, in the weak-coupling regime β > βc, relevant for the continuum limit, our MC results do not support the equivalence of the large-N limits of the lattice chiral model and the corresponding TEK reduction. The implications for the correspondence between TEK model and noncommutative field theory are also discussed.