TY - JOUR

T1 - The quark anti-quark potential and the cusp anomalous dimension from a TBA equation

AU - Correa, Diego

AU - Maldacena, Juan

AU - Sever, Amit

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - 't Hooft and Polyakov loops

KW - AdS-CFT Correspondence

KW - Integrable Field Theories

KW - Scattering Amplitudes

KW - Wilson

UR - http://www.scopus.com/inward/record.url?scp=84865705701&partnerID=8YFLogxK

U2 - 10.1007/JHEP08(2012)134

DO - 10.1007/JHEP08(2012)134

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AN - SCOPUS:84865705701

SN - 1126-6708

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 8

M1 - 134

ER -