The potential of the effective Polyakov line action from the underlying lattice gauge theory

Understand

I adapt a numerical method, previously applied to investigate the Yang-Mills vacuum wavefunctional, to the problem of extracting the effective Polyakov line action from SU(N) lattice gauge theories, with or without matter fields.

• The method can be used to find the variation of the effective Polyakov line action along any trajectory in field configuration space; this information is sufficient to determine the potential term in the action, and strongly constrains the possible form of the kinetic term.
• The technique is illustrated for both pure and gauge-Higgs SU(2) lattice gauge theory at finite temperature.
• A surprise, in the pure gauge theory, is that the potential of the corresponding Polyakov line action contains a non-analytic (yet center-symmetric) term proportional to |P|^3, where P is the trace of the Polyakov line at a given point, in addition to the expected analytic terms proportional to even powers of P.