Integrability of N = 6 Chern-Simons Theory

Arthur E. Lipstein

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Integrability of N = 6 Chern-Simons Theory

Arthur E. Lipstein

High Energy Physics - Theory · Submitted 16 May 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Since then, a great deal of evidence has been accumulated which suggests that the ABJM theory is integrable in the planar limit.

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What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.12 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

In 2008, Aharony, Bergman, Jafferis, and Maldacena (ABJM) discovered a three-dimensional Chern-Simons theory with N = 6 supersymmetry and conjectured that in a certain limit, this theory is dual to type IIA string theory on AdS4xCP3. Since then, a great deal of evidence has been accumulated which suggests that the ABJM theory is integrable in the planar limit. Integrability is a very useful property that allows many physical observables, such as anomalous dimensions and scattering amplitudes, to be computed efficiently. In the first half of this thesis, we will explain how to use integrabilty to compute the anomalous dimensions of long, single-trace operators in the ABJM theory. In particular, we will describe how to compute them at weak coupling using a Bethe Ansatz, and how to compute them at strong coupling using string theory. The latter approach involves using algebraic curve and world-sheet techniques to compute the energies of string states dual to gauge theory operators. In the second half of this thesis, we will discuss integrability from the point of view of on-shell scattering amplitudes in the ABJM theory. In particular, we will describe how to parameterize the amplitudes in terms of supertwistors and how to relate higher-point tree-level amplitudes to lower-point tree-level amplitudes using a recursion relation. We will also explain how this recursion relation can be used to show that all tree-level amplitudes of the ABJM theory are invariant under dual superconformal symmetry. This symmetry is hidden from the point of the action and implies that the theory has Yangian symmetry, which is a key feature of integrability. This thesis is mainly based on the material in [101], [83], and [84].

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In 2008, Aharony, Bergman, Jafferis, and Maldacena (ABJM) discovered a three-dimensional Chern-Simons theory with N = 6 supersymmetry and conjectured that in a certain limit, this theory is dual to type IIA string theory on AdS4xCP3.	background 1.00	0.03	0.04	speculative 0.49
s1	Since then, a great deal of evidence has been accumulated which suggests that the ABJM theory is integrable in the planar limit.	background 1.00	0.04	0.15	hedged possibility 0.99
s2	Integrability is a very useful property that allows many physical observables, such as anomalous dimensions and scattering amplitudes, to be computed efficiently.	background 0.99	0.04	0.04	asserted 1.00
s3	In the first half of this thesis, we will explain how to use integrabilty to compute the anomalous dimensions of long, single-trace operators in the ABJM theory.	contribution 0.85	0.31	0.05	asserted 0.93
s4	In particular, we will describe how to compute them at weak coupling using a Bethe Ansatz, and how to compute them at strong coupling using string theory.	method 0.73	0.33	0.05	asserted 0.97
s5	The latter approach involves using algebraic curve and world-sheet techniques to compute the energies of string states dual to gauge theory operators.	method 0.97	0.15	0.03	asserted 0.98
s6	In the second half of this thesis, we will discuss integrability from the point of view of on-shell scattering amplitudes in the ABJM theory.	contribution 0.86	0.35	0.04	asserted 0.68
s7	In particular, we will describe how to parameterize the amplitudes in terms of supertwistors and how to relate higher-point tree-level amplitudes to lower-point tree-level amplitudes using a recursion relation.	method 0.75	0.42	0.04	asserted 0.88
s8	We will also explain how this recursion relation can be used to show that all tree-level amplitudes of the ABJM theory are invariant under dual superconformal symmetry.	contribution 0.40	0.44	0.13	asserted 0.98
s9	This symmetry is hidden from the point of the action and implies that the theory has Yangian symmetry, which is a key feature of integrability.	interpretation 0.85	0.18	0.12	asserted 1.00
s10	This thesis is mainly based on the material in [101], [83], and [84].	background 0.63	0.07	0.02	asserted 0.99

What kind of paper the classifier reports this is: review 0.89 · evidence from literature 0.94.

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Original abstract

In 2008, Aharony, Bergman, Jafferis, and Maldacena (ABJM) discovered a three-dimensional Chern-Simons theory with N = 6 supersymmetry and conjectured that in a certain limit, this theory is dual to type IIA string theory on AdS4xCP3. Since then, a great deal of evidence has been accumulated which suggests that the ABJM theory is integrable in the planar limit. Integrability is a very useful property that allows many physical observables, such as anomalous dimensions and scattering amplitudes, to be computed efficiently. In the first half of this thesis, we will explain how to use integrabilty to compute the anomalous dimensions of long, single-trace operators in the ABJM theory. In particular, we will describe how to compute them at weak coupling using a Bethe Ansatz, and how to compute them at strong coupling using string theory. The latter approach involves using algebraic curve and world-sheet techniques to compute the energies of string states dual to gauge theory operators. In the second half of this thesis, we will discuss integrability from the point of view of on-shell scattering amplitudes in the ABJM theory. In particular, we will describe how to parameterize the amplitudes in terms of supertwistors and how to relate higher-point tree-level amplitudes to lower-point tree-level amplitudes using a recursion relation. We will also explain how this recursion relation can be used to show that all tree-level amplitudes of the ABJM theory are invariant under dual superconformal symmetry. This symmetry is hidden from the point of the action and implies that the theory has Yangian symmetry, which is a key feature of integrability. This thesis is mainly based on the material in [101], [83], and [84].

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4 arXiv papers cite this in 4 sentences

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Papers citing it · 2 sentences without a confident label

Cites it as background 2 papers

Such integrable structure was also found for the recently proposed duality [ref] between three-dimensional $N=6$ Chern-Simons-matter theory and type IIA theory on $AdS_4×CP^3$ [ref] - [ref] (for reviews see [ref] ).

Note on Integrability of Marginally Deformed ABJ(M) Theories · Introduction · 0.83
The ABJM theory is a conformal field theory [ref] .

Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D · 3D and 4D Grassmannian formulas · 0.99

What it cites · 154 sentences without a confident label

Builds on 1 paper

[ref] and [ref] modulo constraints [ref] .

Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory · Dual Conformal Boost Generator · 0.92

Uses the method or tool of 7 papers

Given that the tree-level amplitudes have dual superconformal symmetry, one can use generalized unitarity methods [ref] to show that the integrands of the cut-constructible loop amplitudes have this symmetry as well [ref] .

Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory · Dual Symmetry of All Tree Amplitudes · 0.81
Given that the tree-level amplitudes have dual superconformal symmetry, one can use generalized unitarity methods [ref] to show that the integrands of the cut-constructible loop amplitudes have this symmetry as well [ref] .

One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits · Dual Symmetry of All Tree Amplitudes · 0.81
Given that the tree-level amplitudes have dual superconformal symmetry, one can use generalized unitarity methods [ref] to show that the integrands of the cut-constructible loop amplitudes have this symmetry as well [ref] .

Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes · Dual Symmetry of All Tree Amplitudes · 0.81

Compares with 3 papers

Note that both sets of frequencies agree with the spectrum of fluctuations that were found in the Penrose limit (up to constant shifts) [ref] .

On Type IIA Penrose Limit and N=6 Chern-Simons Theories · On-Shell Frequencies · 0.95
Note that both sets of frequencies agree with the spectrum of fluctuations that were found in the Penrose limit (up to constant shifts) [ref] .

Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory · On-Shell Frequencies · 0.95
Note that both sets of frequencies agree with the spectrum of fluctuations that were found in the Penrose limit (up to constant shifts) [ref] .

The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory · On-Shell Frequencies · 0.95

Cites as support 10 papers

In particular, the planar dilatation operator in the gauge theory was shown to be integrable up to six loops [ref] , classical integrability was demonstrated in various subsectors of the dual string theory [ref] , an $AdS_4/CFT_3$ algebraic curve was formulated in [ref] , an all-loop Bethe Ansatz was conjectured in [ref] , and a Thermodynamic Bethe Ansatz for the ABJM theory was proposed in [ref] .

Generalized Dynamical Spin Chain and 4-Loop Integrability in N=6 Superconformal Chern-Simons Theory · Introduction · 0.98
In particular, the planar dilatation operator in the gauge theory was shown to be integrable up to six loops [ref] , classical integrability was demonstrated in various subsectors of the dual string theory [ref] , an $AdS_4/CFT_3$ algebraic curve was formulated in [ref] , an all-loop Bethe Ansatz was conjectured in [ref] , and a Thermodynamic Bethe Ansatz for the ABJM theory was proposed in [ref] .

TBA and Y-system for planar $AdS_4/CFT_3$ · Introduction · 0.98
In particular, the planar dilatation operator in the gauge theory was shown to be integrable up to six loops [ref] , classical integrability was demonstrated in various subsectors of the dual string theory [ref] , an $AdS_4/CFT_3$ algebraic curve was formulated in [ref] , an all-loop Bethe Ansatz was conjectured in [ref] , and a Thermodynamic Bethe Ansatz for the ABJM theory was proposed in [ref] .

Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3 · Introduction · 0.98

Cites as background 14 papers

It was then shown by Aharony, Bergman, Jafferis, and Maldacena (ABJM) that in order to generalize the BLG theory to describe an arbitrary number of M2-branes, one must sacrifice maximal supersymmetry [ref] .

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Introduction · 0.85
A nice review of the ABJM spin chain can be found in [ref] .

Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3 · The ABJM Spin Chain · 0.99
The study of superconformal Chern-Simons theories was originally motivated by the need to better understand M-theory, whose fundamental objects are referred to as M2-branes and M5-branes [ref] .

Superconformal Chern-Simons Theories · Introduction · 0.81

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