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Quantum Spectral Curve for a cusped Wilson line in \( \mathcal{N}=4 \) SYM

  • Nikolay Gromov
  • Fedor Levkovich-MaslyukEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We show that the Quantum Spectral Curve (QSC) formalism, initially formulated for the spectrum of anomalous dimensions of all local single trace operators in \( \mathcal{N}=4 \) SYM, can be extended to the generalized cusp anomalous dimension for all values of the parameters. We find that the large spectral parameter asymptotics and some analyticity properties have to be modified, but the functional relations are unchanged. As a demonstration, we find an all-loop analytic expression for the first two nontrivial terms in the small |ϕ ± θ| expansion. We also present nonperturbative numerical results at generic angles which match perfectly 4-loop perturbation theory and the classical string prediction.

The reformulation of the problem in terms of the QSC opens the possibility to explore many open questions. We attach to this paper several Mathematica notebooks which should facilitate future studies.

Keywords

AdS-CFT Correspondence Integrable Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Supplementary material

13130_2016_3781_MOESM1_ESM.nb (22 kb)
ESM 1 Numerical data for the cusp anomalous dimension. Description: This Mathematica notebook contains numerical data for the generalized cusp anomalous dimension, which is shown in the paper in Table 1 (where precision is lowered to fit the page) and on Figure 3. (NB 22 kb)
13130_2016_3781_MOESM2_ESM.nb (95 kb)
ESM 2 Weak coupling expansion of the near-BPS result. Description: This Mathematica notebook contains the tools needed to generate the weak coupling expansion of our all-loop result (3.79) for the anomalous dimension at order (phi-theta)^2 in the near-BPS limit. (NB 94 kb)
13130_2016_3781_MOESM3_ESM.m (6 kb)
ESM 3 Tools for weak coupling solution. Description: This Mathematica notebook contains tools which should be useful for a perturbative weak-coupling solution of the Quantum Spectral Curve. In particular it implements various operations on generalized eta-functions (see Appendix F). (M 5 kb)
13130_2016_3781_MOESM4_ESM.nb (23 kb)
ESM 4 Usage examples for several tools from the file “TwistTools.m”. Description: Demonstrates usage of various functions from TwistTools.m. (NB 23 kb)

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.King’s College London, Department of MathematicsLondonUnited Kingdom
  2. 2.St. Petersburg INPGatchinaRussia

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