Properties of Chiral Wilson Loops

Abstract

We study a class of Wilson Loops in N =4, D=4 Yang-Mills theory belonging to the chiral ring of a N=2, d=1 subalgebra. We show that the expectation value of these loops is independent of their shape. Using properties of the chiral ring, we also show that the expectation value is identically 1. We find the same result for chiral loops in maximally supersymmetric Yang-Mills theory in three, five and six dimensions. In seven dimensions, a generalized Konishi anomaly gives an equation for chiral loops which closely resembles the loop equations of the three dimensional Chern-Simons theory.