Mass generation in the O(3) non-linear σ model

We study the two-point function of the azimuthal angle, G^(φ)(x) = 〈e^iφ(x)e^?iφ(0)〉_inst φ = arg (q¹ + iq²), where q^a is a three-component unit vector field], in the dense instanton gas approximation for the two-dimensional O(3) non-linear σ model. We find that G^(φ) (x) decreases exponentially as |x| → ∞. This suggests that the dense instanton gas may generate a mass gap in the O(3) non-linear σ model. The physical mechanism of this mass generation is also discussed.