Combinatorics of Wilson loops in $\mathcal{N}=4$ SYM theory

Understand

The theory of Wilson loops for gauge theories with unitary gauge groups is formulated in the language of symmetric functions.

• The main objects in this theory are two generating functions, which are related to each other by the involution that exchanges an irreducible representation with its conjugate.
• Both of them contain all information about the Wilson loops in arbitrary representations as well as the correlators of multiply-wound Wilson loops.
• This general framework is combined with the results of the Gaussian matrix model, which calculates the expectation values of $1/2$-BPS circular Wilson loops in $\mathcal{N}=4$ Super-Yang-Mills theory.