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

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.

63 pages, 12 figures. v2: references added, typos corrected

References in corpus (18)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Giant Magnons
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• On String S-matrix, Bound States and TBA
• The all loop AdS4/CFT3 Bethe ansatz
• Wilson Loops of Anti-symmetric Representation and D5-branes
• String hypothesis for the AdS_5 x S^5 mirror
• On the Singularities of the Magnon S-matrix
• Small deformations of supersymmetric Wilson loops and open spin-chains
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• The cusp anomalous dimension at three loops and beyond
• Exact results for static and radiative fields of a quark in N=4 super Yang-Mills
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• Quark-antiquark potential in AdS at one loop
• The spectral problem for strings on twisted AdS_5 x S^5
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Integrable achiral D5-brane reflections and asymptotic Bethe equations

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