Integrability of Orbifold ABJM Theories

De-sheng Li; Hui-Huang Chen; Jun-Bao Wu; Nan Bai; Xiao-Chen Ding

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Integrability of Orbifold ABJM Theories

Nan Bai, Hui-Huang Chen, Xiao-Chen Ding, De-Sheng Li, Jun-Bao Wu

High Energy Physics - Theory · Submitted 22 Jul 2016

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

The authors' main claim In this paper we showed that this remarkable structure survive after orbifold operation with discrete group $\Gamma(\simeq\mathbb{Z}_n)<SU(4)_R\times U(1)_b$.

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Integrable structure has played a very important role in the study of various non-perturbative aspects of planar ABJM theories. In this paper we showed that this remarkable structure survive after orbifold operation with discrete group $\Gamma(\simeq\mathbb{Z}_n)<SU(4)_R\times U(1)_b$. For general $\Gamma$, we prove the integrability in the scalar sector at the planar two-loop order and get the Bethe ansatz equations. The eigenvalues of the anomalous dimension matrix are also obtained. For $\Gamma<SU(4)$, two-loop all-sector and all-loop BAEs are proposed. Supersymmetric orbifolds are discussed in this framework.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Integrable structure has played a very important role in the study of various non-perturbative aspects of planar ABJM theories.	background 1.00	0.05	0.04	asserted 1.00
s1	In this paper we showed that this remarkable structure survive after orbifold operation with discrete group $\Gamma(\simeq\mathbb{Z}_n)<SU(4)_R\times U(1)_b$.	result 0.82	0.94	0.79	asserted 1.00
s2	For general $\Gamma$, we prove the integrability in the scalar sector at the planar two-loop order and get the Bethe ansatz equations.	result 0.68	0.96	0.29	asserted 1.00
s3	The eigenvalues of the anomalous dimension matrix are also obtained.	result 1.00	0.91	0.07	asserted 1.00
s4	For $\Gamma<SU(4)$, two-loop all-sector and all-loop BAEs are proposed.	result 0.74	0.86	0.21	asserted 0.82
s5	Supersymmetric orbifolds are discussed in this framework.	contribution 0.96	0.60	0.04	asserted 0.54

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Original abstract

Integrable structure has played a very important role in the study of various non-perturbative aspects of planar ABJM theories. In this paper we showed that this remarkable structure survive after orbifold operation with discrete group $\Gamma(\simeq\mathbb{Z}_n)<SU(4)_R\times U(1)_b$. For general $\Gamma$, we prove the integrability in the scalar sector at the planar two-loop order and get the Bethe ansatz equations. The eigenvalues of the anomalous dimension matrix are also obtained. For $\Gamma<SU(4)$, two-loop all-sector and all-loop BAEs are proposed. Supersymmetric orbifolds are discussed in this framework.

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6 arXiv papers cite this in 10 sentences

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In order to obtain the scalar sector Bethe equations and to compare with our previous result derived in [ref] , we must do fermionic duality on the Bethe ansatz equations [ref] .

Asymptotic Bethe ansatz of ABJM open spin chain from giant graviton · Reducing to the scalar sector · 0.86
This can be seen by comparing the two proofs for fermionic duality in [ref] and [ref] .] K_1=K_2-K_1, K_3=K_2+K_4+K_4̅-K_3, K_i=K_i, i=2,4,4̅.

Y-system for $\gamma$-deformed ABJM Theory · Duality properties · 0.97

Cites it as background 4 papers

In [ref] , integrability of planar $β$-deformed ABJM theories was established at two-loop order in the scalar sector.[Integrability of a $$-deformation different from the ones in [ref] was also studied in [ref] .] Recently, integrability of orbifold ABJM theories was studied in details in [ref] .

Y-system for $\gamma$-deformed ABJM Theory · Introduction · 0.87
Along similar path, many studies on non-periodic integrable cases re-emerged in the context of ABJM theory [ref] .

Open Spin Chains from Determinant Like Operators in ABJM Theory · Introduction · 0.86
Other studies on the spin chain from three dimensional Chern-Simons-matter theories with less or no supersymmetries include the ones in [ref] .

Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories · Three-dimensional $𝒩=2$ fishnet theories · 0.98

What it cites · 35 sentences without a confident label

Builds on 1 paper

The all loop $AdS_4/CFT_3$ orbifold Bethe equations read, e^-2πimq_1^+η/n =∏_j=1^K_2u_1,k-u_2,j+η/u_1,k-u_2,j-η ∏_j=1^K_41-1/x_1,k x^+η_4,j/1-1/x_1,kx_4,j^-η ∏_j=1^K_4̅1-1/x_1,k x^+η_4̅,j/1-1/x_1,kx_4̅,j^-η , e^-2πimq_2^+η/n =∏_j=1,j≠k^K_2u_2,k-u_2,j-iη/u_2,k-u_2,j+iη ∏_j=1^K_1u_2,k-u_1,j+η/u_2,k-u_1,j-η ∏_j=1^K_3u_2,k-u_3,j+η/u_2,k-u_3,j-η , e^-2πimq_3^+η/n =∏_j=1^K_2u_3,k-u_2,j+η/u_3,k-u_2,j-η ∏_j=1^K_4x_3,k -x^+η_4,j/x_3,k -x^-η_4,j ∏_j=1^K_4̅x_3,k -x^+η_4̅,j/x_3,k -x^-η_4̅,j , e^-2πimq_4^+η/n$x^+_4,k/x^-_4,k$^L = ∏_j=1,j≠k^K_4x^+_4,k-x^-_4,j/x^-η_4,k-x^+η_4,j 1-1/x^+_4,kx^-_4,j/1-1/x^-_4,kx^+_4,jσ_BES(x_ 4,k,x_ 4,j) ∏_j=1^K_11-1/x^-η_4,k x_1,j/1-1/x^+η_4,k x_1,j ×∏_j=1^K_3x^-η_4,k-x_3,j /x^+η_4,k-x_3,j ∏_j=1^K_4̅x^+η_4,k-x^+_4̅,j/x^+_4,k-x^+η_4̅,j σ_BES(x_4,k,x_4̅,j) , e^-2πimq_4̅^+η/n$x^+_4̅,k/x^-_4̅,k$^L =∏_j=1,j≠k^K_4̅ x^+_4̅,k-x^-_4̅,j/x^-η_4̅,k-x^+η_4̅,j 1-1/x^+_4̅,kx^-_4̅,j

The all loop AdS4/CFT3 Bethe ansatz · The all loop Orbifold Bethe equations · 0.96

Uses the method or tool of 2 papers

The all-order asymptotic results are obtained similarly based on all-loop asymptotic BAEs for planar ABJM theory [ref] .

The all loop AdS4/CFT3 Bethe ansatz · Introduction · 0.86
Comparing with the T-matrices for the periodic spin chain, we modify them by inserting two additional matrices $M$ and $M̅$ in the auxiliary spaces $V_0$ and $V_0̅$ so that they can generate the twisted boundary terms in equation ([ref]) [ref] .

Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz · Integrability of Orbifold ABJM Hamiltonian · 0.89

Compares with 1 paper

As an application, we now compare our results with the all-loop BAE equations for the $β$-deformed ABJM theory [ref] .

Y-system for $\gamma$-deformed ABJM Theory · Two applications · 1.00

Cites as support 1 paper

We also confirm these results by using the fact that the orbifold ABJM theory is the low energy effective theory of $N$ membranes placed at the orbifold singularity $ℂ^4/(Γ×ℤ_|Γ|k)$ [ref] .

Aspects of ABJM orbifolds · Introduction · 0.97

Cites as background 13 papers

In this paper, the parent theory is the ABJM theory [ref] which is the low energy effective theory on the worldvolume of N coincident M2-branes at the $ℂ^4/ℤ_k$ orbifold singularity.

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Introduction · 0.82
Both four-dimensional $N=4$ super Yang-Mills (SYM) theory and three-dimensional Aharony-Bergman-Jafferis-Maldacena (ABJM) theory [ref] are integrable in the planar limit [ref] - [ref] .

Integrable Spin Chain in Superconformal Chern-Simons Theory · Introduction · 0.81
Now we will set up some necessary knowledge of orbifold gauge theory and our notation will follow that of [ref] closely.

Bethe Ansatz Equations for General Orbifolds of N=4 SYM · Basic Ingredients of Orbifolding in Gauge Theory · 0.87

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