## Wilson Loops and the Loop Equation by Peter Anderson

**Feb 6, 2017 at 2:00 PM - 3:00 PM**

Host: Prof. Simon Catterall / Contact: Yudaisy Salomón Sargentón, 315-443-5960

202 Physics Bldg.

Pure gauge theories can be formulated in terms of Wilson Loops correlators by

means of the loop equation. In the large-N limit this equation closes in the

expectation value of single loops. In particular, using the lattice as a

regulator, it becomes a well defined equation for a discrete set of loops. Here

we present our development of a numerical method to calculate bounds for the

expectation values of the Wilson loops in both the weak and the strong coupling

regimes. Our method uses the loop equation and the observation that certain

matrices of Wilson Loop expectation values are positive definite. We show how in

the exactly solvable case of two dimensions this approach gives very good

results by considering just a few loops. In four dimensions it gives good

results in the weak coupling region and therefore is complementary to the strong

coupling expansion. Applications to future SUSY lattice studies are then

discussed.