Cusped Wilson lines in symmetric representations

Abstract

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.

Ladder exponentiation for generic large symmetric representation Wilson loops

“…The agreement between the on-shell action and the 1-loop expectation value in the large k limit is indicating that the ladder exponentiation proposed in [18] is correct. We would like to stress that although the spacetime trajectory of the Wilson loop considered is a straight line, the internal space trajectory is kept completely arbitrary.…”

“…In [18] the coincidence between (1) and (2) in the strong coupling limit for large k was verified for a very particular type of Wilson loop. More specifically, this was shown for a Wilson loop defined over a straight line in spacetime with a cusp in one direction of the internal space.…”

“…In the article [18] a limit was proposed to study the expectation value for Wilson loops in large totally symmetric representations of U (N ). More precisely, it was observed that when the rank of the representation k is much larger than the rank of the gauge group N , ladder diagrams 1 dominate over the interaction diagrams in the perturbative expansion.…”

Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension

“…The strong-coupling limit is therefore trivial and we do not find consistency with string theory computation [61]: we argue that the scaling limit considered here does not commute with the strong-coupling limit. Concerning abelian exponentiation, a similar phenomenon has been observed recently [62] in studying N = 4 SYM cusped Wilson loops in k-symmetric representations: at large N and k planar diagrams dominate and the exponentiation is of abelian type.…”

Cusp anomalous dimension and rotating open strings in AdS/CFT

“…We have covered the case when the Wilson loop is in the fundamental representation, a "quark" with mass m q . Could be also worth explore the generalisation to the case of D3-branes [20,21] (symmetric representation) and D5-brane (antisymmetric representation). We plan to investigate this issue in a future work.…”