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Keywords
(7)
bethe ansatz
chernsimons theory
Dispersion Relation
Feynman Diagram
Perturbation Theory
Weak Coupling
Leading Order
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Magnon dispersion to four loops in the ABJM and ABJ models
Magnon dispersion to four loops in the ABJM and ABJ models,10.1088/17518113/43/27/275402,Journal of Physics Amathematical and Theoretical,J. A. Mina
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Magnon dispersion to four loops in the ABJM and ABJ models
(
Citations: 17
)
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J. A. Minahan
,
O. Ohlsson Sax
,
C. Sieg
The ABJM model is a superconformal Chern–Simons theory with supersymmetry which is believed to be integrable in the planar limit. However, there is a couplingdependent function that appears in the magnon
dispersion relation
and the asymptotic
Bethe ansatz
that is only known to
leading order
at strong and weak coupling. We compute this function to four loops in
perturbation theory
by an explicit
Feynman diagram
calculation for both the ABJM model and the ABJ extension. The ABJM fourloop correction has mixed transcendentality, while the ABJ extension adds a term to the ABJM correction with highest transcendentality. We then compute the fourloop wrapping correction for a scalar operator in the 20 representation of SU(4) and find that it agrees with a recent prediction of the ABJM Ysystem by Gromov, Kazakov and Vieira. We also propose a limit of the ABJ model that might be perturbatively integrable at all loop orders but has a short range Hamiltonian.
Journal:
Journal of Physics Amathematical and Theoretical  J PHYS AMATH THEOR
, vol. 43, no. 27, 2010
DOI:
10.1088/17518113/43/27/275402
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Citation Context
(6)
...In ABJ theory one can also study the limit λ � ˆ λ [
31
]...
...In this limit, the Hamiltonian of the SU(2) ×SU(2) sector is, at any loop order, proportional to two decoupled Heisenberg spinchain Hamiltonians [
31
]...
Thomas Klose
.
Review of AdS/CFT Integrability, Chapter IV.3: Chern–Simons and String...
...• The Y system conjectured in [15] for AharonyBergmanJafferisMaldacena [80] theory recently was supported from the 4loop perturbation theory [
81
] at weak coupling...
Nikolay Gromov
.
Ysystem and quasiclassical strings
...The fourloop term in (1.6) was computed in [
14
, 15], where it was found that 1...
...A straightforward extension of the methods in [
14
, 15] to higher loops would lead to a mind boggling number of diagrams...
...Contrast this to the component calculation in [
14
, 15], where one has many times more diagrams...
...1 A different result for h 4(�) in (1.7) was given in earlier versions of [
14
, 15]...
M. Leoni
,
et al.
Superspace calculation of the fourloop spectrum in supersymmetric Che...
...Fourloop gauge theory calculations [
10
, 11] show that h4 = 4 (2) 6:58...
...The gauge theory calculations of [
10
, 11] use the exact dispersion relation and draw Feynman diagrams up to four loops, order 4 ...
Michael C. Abbott
,
et al.
Quantum strings and the AdS 4 /CFT 3 interpolating function
...10 In the flat case and for general momenta, the scalar selfenergy to two loops was calculated in [
56
, 57]...
Mikael Smedbäck
.
On thermodynamics of superconformal ChernSimons theory
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(
Citations: 479
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Journal:
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(
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Journal:
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(
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)
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Sort by:
Citations
(17)
Anomalous dimensions at four loops in N = 6 superconformal Chern–Simons theories
(
Citations: 11
)
J. A. Minahan
,
O. Ohlsson Sax
,
C. Sieg
Journal:
Nuclear Physics B  NUCL PHYS B
, vol. 846, no. 3, pp. 542606, 2011
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(
Citations: 2
)
Matteo Beccaria
,
Fedor LevkovichMaslyuk
,
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Journal of High Energy Physics  J HIGH ENERGY PHYS
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(
Citations: 1
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, pp. 123, 2011
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(
Citations: 26
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Journal:
Journal of High Energy Physics  J HIGH ENERGY PHYS
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Integrability of N=6 ChernSimons theory at six loops and beyond
(
Citations: 10
)
Dongsu Bak
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Hyunsoo Min
,
SooJong Rey
Journal:
Physical Review D  PHYS REV D
, vol. 81, no. 12, 2010