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

By D. Correa, J. Maldacena, A. Sever. 2012

234 citations recorded by the source corpus.

A bstractWe 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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d9e81c566abc2d72f26072e48927cd3f4c96b06e

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In Nuclear and High Energy Physics

1. R. Roiban
2. A. Tseytlin
3. J. Maldacena
4. S. Frolov
5. N. Drukker
6. G. Arutyunov
7. N. Beisert
8. K. Zarembo

Citations in the corpus

• Hexagonalization of correlation functions (2016, background): “Since the (15)See for instance [21, 22], where the same character appears in a different context.”
• Integrable Wilson loops (2012, background): “In [23] it was pointed out that also the replacement”
• Quantum spectral curve for arbitrary state/operator in AdS5/CFT4 (2014, methodology): “Further development of our methods should also allow for a comprehensive description of the open strings spectrum with various types of integrable boundary conditions, which cover such physically relevant cases as quark–anti-quark potential [25, 26], DD̄-systems [27].”
• Towards integrability for AdS 3 / CFT 2 ?> (2014, unknown): “[139–141].”
• Half-BPS Wilson loop and AdS2/CFT1 (2017, background): “In principle, the spectrum of dimensions of operators inserted on the Wilson line should be accessible from the TBA approach of [35,36], and it would be interesting to reproduce our results in this integrability-based framework.”
• Exact results for the entanglement entropy and the energy radiated by a quark (2013, methodology): “If it were possible to also derive an expression for this function using integrability (as it was done for N = 4 super Yang Mills in [18, 19]), then by comparing the two answers one could compute a non-trivial function of the t’Hooft coupling that appears in all the ABJM results obtained via integra”
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory (2015, methodology): “A similar analysis was performed in the study of local operators on a Wilson loop in [33].”