Properties of Chiral Wilson Loops

TL;DR

This paper demonstrates that certain chiral Wilson loops in various supersymmetric Yang-Mills theories have expectation values that are shape-independent and equal to one, revealing deep symmetry properties across dimensions.

Contribution

It establishes the shape independence and exact value of specific chiral Wilson loops in multiple supersymmetric gauge theories, extending known results to higher dimensions.

Findings

Expectation value of chiral Wilson loops is shape-independent.

Expectation value of these loops is identically 1.

Results hold across multiple dimensions, including 3, 4, 5, and 6.

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.