One-loop Structure of Higher Rank Wilson Loops in AdS/CFT

Abstract

The half-supersymmetric Wilson loop in $\mathcal{N}=4$ SYM is arguably the central non-local operator in the AdS/CFT correspondence. On the field theory side, the vacuum expectation values of Wilson loops in arbitrary representations of $SU(N)$ are captured to all orders in perturbation theory by a Gaussian matrix model. Of prominent interest are the $k$-symmetric and $k$-antisymmetric representations, whose gravitational description is given in terms of D3- and D5-branes, respectively, with fluxes in their world volumes. At leading order in $N$ and $\lambda$ the agreement in both cases is exact. In this note we explore the structure of the next-to-leading order correction in the matrix model and compare with existing string theory calculations. We find agreement in the functional dependence on $k$ but a mismatch in the numerical coefficients.

5 pages, one figure. v2: A crucial minus sign acknowledged; agreement now claimed only at the functional level. Changes in abstract and text

References in corpus (8)

• Holographic Wilson Loops
• Wilson Loops of Anti-symmetric Representation and D5-branes
• Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
• The Spectrum of Excitations of Holographic Wilson Loops
• The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling
• A Semiclassical String Description of Wilson Loop with Local Operators
• Semi-classical open string corrections and symmetric Wilson loops
• Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence

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