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Chiral limit of \( \mathcal{N} \) = 4 SYM and ABJM and integrable Feynman graphs

  • João Caetano
  • Ömer Gürdoğan
  • Vladimir Kazakov
Open Access
Regular Article - Theoretical Physics

Abstract

We consider a special double scaling limit, recently introduced by two of the authors, combining weak coupling and large imaginary twist, for the γ-twisted \( \mathcal{N} \) = 4 SYM theory. We also establish the analogous limit for ABJM theory. The resulting non-gauge chiral 4D and 3D theories of interacting scalars and fermions are integrable in the planar limit. In spite of the breakdown of conformality by double-trace interactions, most of the correlators for local operators of these theories are conformal, with non-trivial anomalous dimensions defined by specific, integrable Feynman diagrams. We discuss the details of this diagrammatics. We construct the doubly-scaled asymptotic Bethe ansatz (ABA) equations for multi-magnon states in these theories. Each entry of the mixing matrix of local conformal operators in the simplest of these theories — the bi-scalar model in 4D and tri-scalar model in 3D — is given by a single Feynman diagram at any given loop order. The related diagrams are in principle computable, up to a few scheme dependent constants, by integrability methods (quantum spectral curve or ABA). These constants should be fixed from direct computations of a few simplest graphs. This integrability-based method is advocated to be able to provide information about some high loop order graphs which are hardly computable by other known methods. We exemplify our approach with specific five-loop graphs.

Keywords

Conformal Field Theory 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.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • João Caetano
    • 1
  • Ömer Gürdoğan
    • 1
    • 2
  • Vladimir Kazakov
    • 1
  1. 1.Laboratoire de Physique Théorique de l’Ecole Normale Supérieure et l’Université Paris-VIParis CEDEXFrance
  2. 2.School of Physics & AstronomyUniversity of SouthamptonSouthamptonU.K.

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