# CTMP Seminar: Symmetries in high energy QCD: Wilson lines and representations of SU(N)

Judith Alcock-Zeilinger

UCT Department of Physics

Symmetries in high energy QCD: Wilson lines and representations of SU(N)

QCD reaction channels dominate particle production in modern collider experiments. In the small Bjorken-x limit of high energy QCD, the number of gluons produced is so large that these gluons dominate the initial conditions of such processes; these initial gluon dominated configurations are called the color glass condensate (CGC). The theoretical foundation of the CGC treatment are factorisation theorems that allow one to separate hard and soft contributions. In particular, the interaction between a hard projectile with the CGC occurs via the exchange of soft gluons. Such an interaction is said to be eikonal and is described by path-ordered exponentials in the gauge group SU(N) called Wilson lines. These Wilson lines, by virtue of being elements of SU(N), impart additional structure on the parton configurations within the projectile in the interactions of interest. In particular, these partons need to assemble into singlet states of SU(N).

In this talk, a short overview of eikonal interactions and the color glass condensate will be given. This motivates the subsequent discussion on the representation theory of SU(N): A quick review of the irreducible representations of SU(N) over an only-quark Fock space, with a particular focus on tableaux, is given. A Hermitian version of the standard Young projection operators, and transition operators between equivalent irreducible representations are introduced, and it is discussed how these objects help generate the singlet states of SU(N) over Fock spaces of an arbitrary number of quarks, antiquarks and gluons. These singlet states are then used to construct Wilson line correlators. I end with a brief comment on higher dimensional representations of SU(N), highlighting the necessity of further research on the matter.

Duncan Elliot Seminar Room

RW James Building