Abstract
We consider the classical limit of the recently obtained exact near-BPS result for the anomalous dimension of a cusped Wilson line with the insertion of an operator with L units of R-charge at the cusp in planar \( \mathcal{N} \) = 4 SYM. The classical limit requires taking both the ’t Hooft coupling and L to infinity. Since the formula for the cusp anomalous dimension involves determinants of size proportional to L, the classical limit requires a matrix model reformulation of the result. Building on results of Gromov and Sever, we construct such a matrix model-like representation and find the corresponding classical algebraic curve. Using this we find the classical value of the cusp anomalous dimension and the 1-loop correction to it. We check our results against the energy of the classical solution and numerically by extrapolating from the quantum regime of finite L.
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ArXiv ePrint: 1306.2527
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Sizov, G., Valatka, S. Algebraic curve for a cusped Wilson line. J. High Energ. Phys. 2014, 149 (2014). https://doi.org/10.1007/JHEP05(2014)149
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DOI: https://doi.org/10.1007/JHEP05(2014)149