Sky Cao: Expanded regimes of area law for lattice Yang-Mills theories

I will discuss a recent result which extends the parameter regimes for which Wilson’s area law is proven for pure U(N) lattice Yang– Mills theories, in particular when N is large. This improves on a classical result of Osterwalder-Seiler from 1978. To do so, we view the master loop equation as a linear inhomogeneous equation for Wilson string expectations, and then prove an a priori bound for solutions to the equation. Joint work with Ron Nissim and Scott Sheffield.