Simultaneous lattice-mesh and large-N limits

Determine whether taking the large-N limit and the lattice-mesh limit simultaneously can produce a non-trivial scaling limit for two-dimensional lattice Yang–Mills theory with the Wilson action.

Background

The paper argues heuristically that, for the Wilson-action lattice Yang–Mills model, taking the lattice mesh to zero after taking the large-N limit yields only trivial Wilson loop limits under any rescaling of the inverse-temperature parameter. This suggests that the order of the N→∞ and lattice-mesh limits may be responsible for the discrepancy with two-dimensional continuum Yang–Mills theory.

The unresolved issue is whether a joint limiting procedure, rather than sequential limits, can avoid this trivialization and recover a non-trivial continuum theory.