Cusped Wilson lines in symmetric representations

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 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√λ≫ 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≫ N, the cusped Wilson line expectation value is simply given by the exponential of the 1-loop diagram. Using group theory arguments, this eikonal exponentiation is conjectured to take place for all Wilson loop operators in symmetric representations with large k, independently of the contour on which they are supported.