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Journal of High Energy Physics

, 2016:90 | Cite as

Two-loop SL(2) form factors and maximal transcendentality

  • Florian LoebbertEmail author
  • Christoph Sieg
  • Matthias Wilhelm
  • Gang Yang
Open Access
Regular Article - Theoretical Physics

Abstract

Form factors of composite operators in the SL(2) sector of \( \mathcal{N} \) = 4 SYM theory are studied up to two loops via the on-shell unitarity method. The non-compactness of this subsector implies the novel feature and technical challenge of an unlimited number of loop momenta in the integrand’s numerator. At one loop, we derive the full minimal form factor to all orders in the dimensional regularisation parameter. At two loops, we construct the complete integrand for composite operators with an arbitrary number of covariant derivatives, and we obtain the remainder functions as well as the dilatation operator for composite operators with up to three covariant derivatives. The remainder functions reveal curious patterns suggesting a hidden maximal uniform transcendentality for the full form factor. Finally, we speculate about an extension of these patterns to QCD.

Keywords

Scattering Amplitudes Conformal Field Theory Integrable Field Theories Supersymmetric Gauge Theory 

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.

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Florian Loebbert
    • 1
    Email author
  • Christoph Sieg
    • 1
    • 2
  • Matthias Wilhelm
    • 1
    • 2
    • 3
  • Gang Yang
    • 4
    • 1
  1. 1.Institut für PhysikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Niels Bohr InstituteCopenhagen UniversityCopenhagen ØDenmark
  4. 4.CAS Key Laboratory of Theoretical Physics, Institute of Theoretical PhysicsChinese Academy of SciencesBeijingChina

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