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 $\mathcal{N}=4$ 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. 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.

24 pages, 6 figures; v2: improved figures and references added

References in corpus (7)

• Holographic Wilson Loops
• Wilson Loops of Anti-symmetric Representation and D5-branes
• Supersymmetric Wilson loops on S^3
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Two-loop cusp anomaly in ABJM at strong coupling
• Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM
• Exact probes of orientifolds

Cited by in corpus (6)

• Spin Impurities, Wilson Lines and Semiclassics
• Wilson loop in general representation and RG flow in 1d defect QFT
• Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
• Scalar Insertions in Cusped Wilson Loops in the Ladders Limit of Planar N=4 SYM
• Cusp Anomalous dimension and rotating open strings in AdS/CFT
• Ladder exponentiation for generic large symmetric representation Wilson loops