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Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs

Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs
Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs

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 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.

Conformal Field Theory, Integrable Field Theories
1126-6708
1-42
Caetano, João
71ef3e3f-58cf-4462-81b8-2e51589628ce
Gürdoğan, Ömer
841de8b6-4eb2-407f-a4c4-c8136403794d
Kazakov, Vladimir
1273b14e-210e-4720-9d5e-0f96f1982c91
Caetano, João
71ef3e3f-58cf-4462-81b8-2e51589628ce
Gürdoğan, Ömer
841de8b6-4eb2-407f-a4c4-c8136403794d
Kazakov, Vladimir
1273b14e-210e-4720-9d5e-0f96f1982c91

Caetano, João, Gürdoğan, Ömer and Kazakov, Vladimir (2018) Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs. The Journal of High Energy Physics, 2018 (3), 1-42. (doi:10.1007/JHEP03(2018)077).

Record type: Article

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 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.

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a10.1007%2FJHEP03(2018)077
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Accepted/In Press date: 6 March 2018
e-pub ahead of print date: 13 March 2018
Keywords: Conformal Field Theory, Integrable Field Theories

Identifiers

Local EPrints ID: 419335
URI: https://eprints.soton.ac.uk/id/eprint/419335
ISSN: 1126-6708
PURE UUID: 3dc2050e-a50e-46cb-802c-ff6bd57c9ec3

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Date deposited: 11 Apr 2018 16:30
Last modified: 13 Mar 2019 18:38

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