Constraints on the IR behavior of the gluon propagator in Yang-Mills theories

Understand

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field.

• This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions.
• In the two-dimensional case we find D(0) = 0, in agreement with Ref.
• [1].