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The quark anti-quark potential and the cusp anomalous dimension from a TBA equation

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Abstract

We derive a set of integral equations of the TBA type for the generalized cusp anomalous dimension, or the quark antiquark potential on the three sphere, as a function of the angles. We do this by considering a family of local operators on a Wilson loop with charge L. In the large L limit the problem can be solved in terms of a certain boundary reflection matrix. We determine this reflection matrix by using the symmetries and the boundary crossing equation. The cusp is introduced through a relative rotation between the two boundaries. Then the TBA trick of exchanging space and time leads to an exact equation for all values of L. The L = 0 case corresponds to the cusped Wilson loop with no operators inserted. We then derive a slightly simplified integral equation which describes the small angle limit. We solve this equation up to three loops in perturbation theory and match the results that were obtained with more direct approaches.

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Authors and Affiliations

  1. Instituto de Física La Plata, Universidad Nacional de La Plata, C.C. 67, 1900, La Plata, Argentina

    Diego Correa

  2. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.

    Juan Maldacena & Amit Sever

  3. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2J 2W9, Canada

    Amit Sever

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  1. Diego Correa
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  2. Juan Maldacena
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  3. Amit Sever
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Correspondence to Amit Sever.

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ArXiv ePrint: 1203.1913

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Correa, D., Maldacena, J. & Sever, A. The quark anti-quark potential and the cusp anomalous dimension from a TBA equation. J. High Energ. Phys. 2012, 134 (2012). https://doi.org/10.1007/JHEP08(2012)134

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