Cusped Wilson lines in symmetric representations

Understand

We study the cusped Wilson line operators and Bremsstrahlung functions associated to particles transforming in the rank-$k$ symmetric representation of the gauge group $U(N)$ for ${\cal N} = 4$ super Yang-Mills.

• We find the holographic D3-brane description for Wilson loops with internal cusps in two different limits: small cusp angle and $k\sqrt{\lambda}\gg N$.
• This allows for a non-trivial check of a conjectured relation between the Bremsstrahlung function and the expectation value of the 1/2 BPS circular loop in the case of a representation other than the fundamental.
• Moreover, we observe that in the limit of $k\gg N$, the cusped Wilson line expectation value is simply given by the exponential of the 1-loop diagram.