Pith. sign in

REVIEW 1 major objections 8 minor 61 references

Monodromy defects in ABJM theory and integrability

T0 review · 1 major / 8 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Supersymmetric monodromy defects in ABJM theory, known as vortex loops, are integrable boundary states of the alternating SU(4) spin chain, and the leading one-point functions of non-protected scalar operators are given by a single closed…

desk verdict A solid integrability calculation extending the overlap machinery to ABJM monodromy defects, but the claimed closed form has a genuine gap in the unpaired-zero-root sector. read the letter →

arxiv 2608.10840 v1 pith:6E6XNYUJ submitted 2026-08-11 hep-th

Charlotte Kristjansen , Andrey Shusharin This is my paper · ORCID
classification hep-th
keywords ABJMtheorymonodromydefectsvortexloopsone-pointfunctionsintegrableboundarystatesKTrelationalternatingSU(4)spinchainBaxterpolynomials
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper establishes that the supersymmetric monodromy defects of ABJM theory—line defects around which scalar fields wind, also called vortex loops—are integrable boundary states of the planar alternating SU(4) spin chain. Solving the KT relation of the algebraic Bethe ansatz for the matrix product state representing the defect, the authors obtain one closed formula for the leading-order one-point function of every non-protected single-trace scalar operator in these backgrounds. The normalized overlap is a product of Baxter polynomials evaluated at half-integer arguments, powers of the defect parameters, and the Gaudin superdeterminant, together with selection rules that decide which operators couple to the defect. This matters because one-point functions of non-protected operators in defect theories are normally accessible only state by state; here the whole class collapses to a single expression, with the giant-graviton three-point overlap and a class of Wilson-loop one-point functions emerging as special cases. The paper also initiates quantization in the defect background and computes the first quantum correction in the simplest setting.

What carries the argument

The engine is the KT relation, the consistency equation between a boundary reflection matrix and the spin-chain monodromy matrix that makes a matrix product state an integrable boundary state. It is applied to the two-site building block (one fundamental and one anti-fundamental site) of the alternating SU(4) chain. The defect data enter through the $K$-matrix solution $K_{ij}(u)=\delta_{ij}+\frac{2u}{1-u}\frac{\beta_i^*\beta_j}{|\beta|^2}$, from which nested $G$- and $F$-functions are constructed; their products reorganize into the Baxter polynomials $Q_1(i/2)$, $Q_2(0)$, and $Q_2(i/2)$ in the final overlap. Because a nested component of the $K$-matrix vanishes, a deformation with a free parameter $b_1$ is needed, and demanding independence from this regularization enforces the extra selection rule $r_1=r_2$. The square root of the Gaudin superdeterminant, $\sqrt{\mathrm{Sdet}G}$, is the universal normalization factor independent of the defect. The same machinery supports the fermionic-duality extension to the all-loop $\mathfrak{osp}(4|6)$ Dynkin diagram.

What would settle it

Compute the leading-order one-point function of a length-$L=4$ non-protected scalar operator in the vortex-loop background directly in ABJM field theory and compare it with the closed formula; any discrepancy would show that the regularization or zero-root prescription misses certain sectors. A second, cheaper check: find a Bethe state that violates $r_1=r_2$ but has a non-vanishing direct overlap with the matrix product state, which would falsify the selection rule on which the formula depends.

Watch

Extended reading notes

Core claim

The central discovery is that a supersymmetric monodromy defect in ABJM theory corresponds to an integrable matrix product state of the alternating SU(4) spin chain, and the leading semi-classical one-point function of any non-protected scalar operator follows from one closed expression. For a Bethe eigenstate $|u\rangle$ with root numbers $r_1,r_2,r_3$ satisfying the selection rules $r_1=r_2=r_3$, and additionally $L=r_1$ when $\beta_4=0$, the normalized overlap reads $$\frac{\langle \mathrm{MPS}|u\rangle}{\sqrt{\langle u|u\rangle}} = (\beta_1\beta_4^*)^{L-r_1}\,|\$\beta$|^{2r_1}\,$2^{{-r_1}}$\,(-i)^{r_1}\,\frac{Q_1(i/2)}{\sqrt{Q_2(0)\,Q_2(i/2)}}\,\sqrt{\mathrm{Sdet}\,G},$$ with $Q_a(u)=\prod_j(u-u^{(a)}_j)$ the Baxter polynomial of node $a$. The one-point function is this overlap multiplied by the prefactor $1/(|z|^L\lambda^L L^{1/2})$. The same formula reproduces the overlap for two maximal giant gravitons and a tiny graviton and, up to a phase, the scalar one-point functions for a class of supersymmetric Wilson loops. In the simplest quantum background the first correction multiplies every one-point function by the universal factor $1-2L\lambda/(\pi|\beta|^2)+\cdots$.

Load-bearing premise

The load-bearing premise is that the KT-relation recipe, including the regularized $K$-matrix and the treatment of unpaired zero roots, correctly computes the overlap for every Bethe state; the paper verifies the formula explicitly only for operators of length $L=2$ and $L=3$, and in the $L=3$ case with a zero root a free parameter is fixed by matching a field-theory result rather than derived.

Editorial extensions

If this is right

  • All leading-order one-point functions of non-protected scalar operators in the 1/2-, 1/3-, and 1/6-BPS monodromy backgrounds are governed by one formula, so overlaps no longer need to be computed operator by operator.
  • The known giant-graviton three-point overlap and the scalar one-point functions for a class of supersymmetric Wilson loops are recovered as special cases of the same expression.
  • The fermionic-duality argument predicts a factorized overlap on the all-loop $\mathfrak{osp}(4|6)$ Dynkin diagram, which is a first indication of higher-loop integrability for these one-point functions.
  • In the simplest quantum background the first correction is the universal factor $1-2L\lambda/(\pi|\beta|^2)+\cdots$, independent of the detailed structure of the operator at this order.
  • The spectrum of conformal dimensions of gauge-invariant bulk operators is unchanged by the defect, and gauge-invariant correlation functions remain single-valued despite the monodromy of the underlying fields.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A sharp testable consequence: for the 1/2- and 1/3-BPS defects ($\beta_4=0$), the selection rule $L=r_1$ restricts non-vanishing one-point functions to a specific class of Bethe states, and a direct field-theory computation of a length-four operator would probe this restriction.
  • The same $K$-matrix has also appeared in a systematic search for integrable boundary states of the ABJM spin chain, so the vortex-loop overlaps are likely members of a larger family of boundary states, some of which may correspond to as-yet-unidentified defects or Wilson-loop-like observables.
  • Because the first quantum correction comes only from a tadpole, one may conjecture that the one-point functions exponentiate to a closed all-order factor in the simple background; a two-loop computation would either confirm the pattern or reveal where it breaks.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 8 minor

Summary. The manuscript studies co-dimension-two supersymmetric monodromy defects (``vortex loops'') in ABJM theory. Its central result is a claimed closed-form expression for the leading-order one-point functions of non-protected scalar operators, obtained by representing the defect as a matrix product state, solving the uncrossed KT relation for the reflection matrix (3.17), and applying Gombor's nested-K-matrix formalism with a deformation (3.31)-(3.32) that regularizes a vanishing intermediate entry. The resulting overlap (3.43), combined with the prefactor (3.11), involves only the Baxter polynomials Q1(i/2), Q2(0), Q2(i/2) and the Gaudin superdeterminant, subject to the selection rules r1=r3, r1=r2, and L=r1 for beta4=0. The paper shows that this formula reduces to the previously known giant-graviton three-point-function overlap (3.49) and to certain Wilson-loop one-point-function overlaps (3.51), and Appendix A checks the formula against direct field theory for an L=2 and an L=3 operator. Section 4 initiates quantization around the defect in the unit-matrix-VEV case, computing a renormalized tadpole (B.12) and the first quantum correction (4.30); Section 5 speculatively extends the formula to the all-loop osp(4|6) Dynkin diagram via fermionic dualities.

Significance. If fully established, the main result is a genuine advance: it unifies the one-point functions of non-protected scalar operators for the three classes of monodromy defects (1/2-, 1/3-, 1/6-BPS) into the single closed formula (3.43) with the block generalization (3.45), and it recovers the previously known giant-graviton overlap [26] and Wilson-loop overlaps [27] as special cases. The derivation has real substance: it proceeds from the KT relation with an explicit regularized K-matrix (3.31)-(3.32) and derives the selection rules r1=r3, r1=r2, L=r1 rather than assuming them, and it is not circular, since nothing in the final formula was defined to reproduce [26] or [27]. The Appendix A checks are genuine field-theory computations for two short operators, and the formula (3.43) is falsifiable, for instance by Bethe-ansatz numerics for longer states. Section 4's first quantum correction, though restricted to the unit-matrix-VEV case, is a concrete and reproducible computation with a transparent scheme, and Section 5 is appropriately hedged as a speculation.

major comments (1)
  1. [Section 3, Eq. (3.43); Appendix A, Eqs. (A.9)-(A.12)] The claimed closed form is not established for Bethe states with an unpaired zero root at the middle node, and the resulting gap is larger than a corner case. The denominator of (3.43) contains Q2(0), which vanishes whenever one of the u^{(2)} roots is zero; such states satisfy the selection rules, since u=0 is self-paired under u -> -u and (3.18)/(3.42) do not forbid odd r2. Indeed the derivation itself presupposes even r2, since (3.40) contains a product over r2/2. For the beta4=0 cases the rules (3.42) and (3.44) imply r1=r2=L, so every odd-L operator belongs to the Q2(0)=0 sector. Appendix A treats the L=3 state (A.9) by declaring that the unpaired zero root 'requires special treatment': a free parameter gamma is introduced, set proportional to b1 with unit proportionality constant, the zero root is omitted from the Baxter polynomial, and an unexplained overall sign is then dropped in arriving at (A.12). This prescription is calibrated to the single field-theory result (A.8), not derived from the KT relation. The abstract's claim of a closed-form expression for all one-point functions is therefore supported only on the even-r2, Q2(0) != 0 sector; the odd-r2 sector rests on one fitted example. The authors should either extend the KT derivation to cover the zero-root sector or explicitly restrict the claim and present the zero-root rule as an empirically supported conjecture.
minor comments (8)
  1. [Section 1 and throughout] 'Subsquently' (p. 2) should be 'Subsequently'; similar typos appear later, notably 'auxillary' after Eq. (3.17), 'mondromy' and 'the the interplay' in Section 6, and 'read of from' in Appendix A.
  2. [Eqs. (3.40)-(3.41)] The overlap formula is split across two displayed equations with a dangling multiplication sign; a single display would prevent misreading of the power structure.
  3. [Section 3, Eq. (3.51)] The comparison with [27] is worded confusingly: 'which up to a phase which agrees with the result of [27]' should be rewritten as a single clear statement of the phase agreement.
  4. [Appendix A, Eqs. (A.11)-(A.12)] The overall sign (-1) removed before (A.12) is stated without explanation; please clarify whether this is a phase convention of the Bethe-state normalization or part of the zero-root prescription, since the L=2 check did not require it.
  5. [Section 4, Eq. (4.23) and Appendix B] The half-integer monodromy assigned to the quantum fluctuation of Y^1 is an input to the tadpole computation (B.12); the single-valuedness argument for the Lagrangian is plausible, but the text should state explicitly whether this monodromy is a definition of the quantized defect theory or a derived consistency condition, and the subtraction in (B.4) should be identified as a renormalization-scheme choice.
  6. [Section 4, Eq. (4.30)] The combinatorial origin of the factor 2L in the tadpole correction is not spelled out; a sentence on the counting of contraction channels would make the result checkable.
  7. [Section 5, Figure 2] The schematic Dynkin-diagram figure must be redrawn with clear node numbering and unambiguous numerator/denominator markings; the current ASCII version cannot be parsed reliably.
  8. [References] Reference [8] cites an unpublished talk; please replace it with a published source if one exists.

Circularity Check

1 steps flagged · score 4.0 of 10

Main KT-relation derivation is independent, but the claimed closed form on the unpaired-zero-root sector is verified only after fitting a free parameter to the field-theory result.

  1. fitted input called prediction [Appendix A, around Eqs. (A.9)-(A.12); affects the claimed universal formula Eq. (3.43)]
    "The unpaired zero-root at the middle (chiral) node requires special treatment. ... In our case we fix the parameter to be proportional to b1 which is necessary to get a finite result, and we observe that we get agreement with the field theory computation if the constant of proportionality is simply set equal to one. This corresponds to leaving out the single zero root when evaluating the Baxter polyomial which is a strategy that has worked in many other cases as well, se e.g. [24]."

    The general formula (3.43) contains the factor 1/sqrt(Q2(0)Q2(i/2)). For the L=3 state (A.9), the node-2 Bethe roots are {2sqrt(3)alpha, -2sqrt(3)alpha, 0}, so Q2(0)=0 and the literal formula diverges. The paper does not test (3.43) in this sector; instead it introduces a free parameter gamma, sets its proportionality constant to one in order to reproduce the field-theory result (A.8), and omits the zero root from the Baxter polynomial. The subsequent 'agreement' in (A.12) is therefore a calibration, not an independent verification. Since the selection rules (3.18) and (3.42) permit unpaired zero roots at the middle node and the paper claims a closed form encompassing all one-point functions, this fitted sector is load-bearing and the derivation does not establish the formula there.

full rationale

The central derivation of the overlap formula (3.43) is not circular: it follows from the KT relation with the K-matrix (3.17), using the Gombor machinery [22,23], and the K-matrix itself is independently reported in [30]. The final expression is not defined to reproduce the giant-graviton or Wilson-loop results; those appear as special cases and are compared with earlier work. The L=2 verification in Appendix A is an independent field-theory check. The only genuinely circular piece is the treatment of the unpaired zero root in the L=3 check: the general formula is singular there, and the matching result is obtained by fixing a free parameter to the known field-theory value and omitting the problematic root. This does not collapse the whole derivation, but it does weaken the claim that (3.43) is a derived closed form valid for all Bethe states, because the Q2(0)=0 sector is load-bearing for that 'all' claim and rests on one fitted example rather than on the KT derivation. Section 5 is explicitly speculative and not load-bearing for the main result.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central formula rests on the standard integrability mapping of planar ABJM theory and on the KT-relation overlap framework of Gombor. No fitted constant enters the main formula; the two regularization and free parameters (b1, gamma) are derivation tools, and gamma is fixed only in the L=3 verification. The defect parameters beta_i are physical inputs, not fitting parameters.

free parameters (2)
  • b1 (K-matrix regularization parameter) = eliminated; final result independent only when r1=r2
    Introduced in (3.31) to regularize the nested K-matrix singularity; the final formula is independent of b1 only after imposing the selection rule r1=r2, so it is a derivation tool, not a physical parameter.
  • gamma (zero-root constant) = 1
    In Appendix A, for the L=3 state with an unpaired zero Bethe root, the overlap method introduces a free parameter gamma; the paper fixes the proportionality constant to 1 by matching the field-theory one-point function. This parameter affects the verification, not the general formula itself.
assumptions (6)
  • domain assumption Planar ABJM single-trace operators are described by the two-loop alternating SU(4) spin chain (3.3) with Bethe equations (3.8).
    Used throughout Section 3; this is the standard integrability map (Minahan-Zarembo) that the authors rely on without re-derivation.
  • domain assumption Leading-order one-point functions are given by the MPS overlap formula (3.11), i.e. classical fields substituted into operators.
    Central computational premise; standard in defect CFT integrability and cited to [33,34].
  • domain assumption The Gombor KT-relation framework, including the general overlap formula (3.20) with SdetG, applies to this boundary problem.
    The derivation of the K-matrix and F-functions depends on the results of [22,23]; the paper solves the KT relation but does not prove the framework.
  • ad hoc to paper The K-matrix deformation (3.31)-(3.32) with free parameters b_k regularizes the nested K-matrix singularities and can be used to extract the overlap.
    The specific deformation is adopted from [23] and applied here; its validity for this defect is assumed, and the selection rule r1=r2 follows from requiring b1-independence.
  • ad hoc to paper Quantum fluctuations of Y^1 around the 1/2-BPS defect carry the same half-integer monodromy as the classical background (4.23).
    Needed for the tadpole computation in Section 4; it makes the Lagrangian single valued but is a physical choice not derived from the leading-order overlap.
  • domain assumption Fermionic dualities preserve the factorized form of the overlap formula (Section 5).
    The extension to the all-loop Dynkin diagram assumes the covariance of SdetG and the factorized form, an assumption noted in [41] to sometimes fail.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Monodromy defects in ABJM theory and integrability." pith.science (2026). https://pith.science/paper/6E6XNYUJ

@misc{pith2026260810840,
  author       = {Pith},
  title        = {Pith review of: Monodromy defects in ABJM theory and integrability},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6E6XNYUJ}},
  note         = {Machine review of arXiv:2608.10840}
}
read the original abstract

We establish that supersymmetric monodromy defects in ABJM theory, also known as vortex loops, define integrable boundary states of the underlying alternating SU(4) spin chain. Exploiting the KT relation within the framework of the algebraic Bethe ansatz, we derive a closed-form expression for the leading-order one-point functions of non- protected operators in the presence of these defects. As a special case, our result reproduces the spin-chain overlap governing the three-point functions of two maximal giant gravitons and a single tiny graviton. We furthermore investigate the quantization of the theory in the defect background and compute the first quantum correction to the one-point functions in the simplest setting. Finally, we discuss possible extensions of our overlap formula.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

61 extracted references · 14 canonical work pages

  1. [30]

    N. Bai, H. Yang and M.-Z. Shao,Solving for the integrable boundary states of the ABJM spin chain fromKT-relations,2607.04203

    work page Pith review arXiv

  2. [26]

    P. Yang, Y. Jiang, S. Komatsu and J.-B. Wu,Three-point functions in ABJM and Bethe Ansatz,JHEP01(2022) 002 [2103.15840]

    arXiv 2022

  3. [27]

    Jiang, J.-B

    Y. Jiang, J.-B. Wu and P. Yang,Wilson-loop one-point functions in ABJM theory,JHEP09 (2023) 047 [2306.05773]

    arXiv 2023

  4. [1]

    Gukov and E

    S. Gukov and E. Witten,Rigid Surface Operators,Adv. Theor. Math. Phys.14(2010) 87 [0804.1561]

    arXiv 2010

  5. [2]

    Gukov and E

    S. Gukov and E. Witten,Gauge Theory, Ramification, And The Geometric Langlands Program,hep-th/0612073

    arXiv

  6. [3]

    Drukker, J

    N. Drukker, J. Gomis and S. Matsuura,Probing N=4 SYM With Surface Operators,JHEP 10(2008) 048 [0805.4199]

    arXiv 2008

  7. [4]

    Gukov,Surface operators., inNew Dualities of Supersymmetric Gauge Theories, J

    S. Gukov,Surface operators., inNew Dualities of Supersymmetric Gauge Theories, J. Teschner, ed., pp. 223–259 (2016), DOI [1412.7127]

    arXiv 2016

  8. [5]

    C. Choi, J. Gomis and R. Izquierdo Garc ´ ıa,Surface operators and exact holography,JHEP 12(2024) 195 [2406.08541]

    arXiv 2024

Show all 61 references
  1. [6]

    Holguin and H

    A. Holguin and H. Kawai,Integrability and conformal blocks for surface defects inN= 4 SYM,JHEP11(2025) 043 [2503.09944]

    2025

  2. [7]

    Chalabi, C

    A. Chalabi, C. Kristjansen and C. Su,Integrable corners in the space of Gukov-Witten surface defects,Phys. Lett. B866(2025) 139512 [2503.22598]

    2025 arXiv

  3. [8]

    Analytic bootstrap for holographic surface defect

    L. Bianchi, “Analytic bootstrap for holographic surface defect.” Talk presented at the Workshop Defects and Extended Excitations in Quantum Field Theory, Quantum Matter and Statistical Models, Florence, Italy, May, 2026

    2026

  4. [9]

    Andrei et al.,Boundary and Defect CFT: Open Problems and Applications,J

    N. Andrei et al.,Boundary and Defect CFT: Open Problems and Applications,J. Phys. A53 (2020) 453002 [1810.05697]

    2020 arXiv

  5. [10]

    Dixon, J.A

    L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten,Strings on orbifolds,Nucl. Phys. B261 (1985) 678

    1985

  6. [11]

    Dixon, D

    L.J. Dixon, D. Friedan, E.J. Martinec and S.H. Shenker,The conformal field theory of orbifolds,Nucl. Phys. B282(1987) 13

    1987

  7. [12]

    S¨ oderberg,Anomalous Dimensions in the WF O(N) Model with a Monodromy Line Defect,JHEP03(2018) 058 [1706.02414]

    A. S¨ oderberg,Anomalous Dimensions in the WF O(N) Model with a Monodromy Line Defect,JHEP03(2018) 058 [1706.02414]

    2018 arXiv

  8. [13]

    Giombi, E

    S. Giombi, E. Helfenberger, Z. Ji and H. Khanchandani,Monodromy defects from hyperbolic space,JHEP02(2022) 041 [2102.11815]

    2022 arXiv

  9. [14]

    Lauria, P

    E. Lauria, P. Liendo, B.C. Van Rees and X. Zhao,Line and surface defects for the free scalar field,JHEP01(2021) 060 [2005.02413]

    2021 arXiv

  10. [15]

    Bianchi, A

    L. Bianchi, A. Chalabi, V. Proch´ azka, B. Robinson and J. Sisti,Monodromy defects in free field theories,JHEP08(2021) 013 [2104.01220]

    2021 arXiv

  11. [16]

    Gomis,The AdS/C-P-TCorrespondence,2507.12467

    J. Gomis,The AdS/C-P-TCorrespondence,2507.12467

    arXiv

  12. [17]

    Drukker, J

    N. Drukker, J. Gomis and D. Young,Vortex Loop Operators, M2-branes and Holography, JHEP03(2009) 004 [0810.4344]. – 27 –

    2009 arXiv

  13. [18]

    Ambrosino, J

    F. Ambrosino, J. Gomis and S.R. Kannagi,Monodromy defects in Chern-Simons theory and Holography,2607.06669

    arXiv

  14. [19]

    Minahan and K

    J.A. Minahan and K. Zarembo,The Bethe ansatz for superconformal Chern-Simons,JHEP 09(2008) 040 [0806.3951]

    2008 arXiv

  15. [20]

    De Leeuw, T

    M. De Leeuw, T. Gombor, C. Kristjansen, G. Linardopoulos and B. Pozsgay,Spin Chain Overlaps and the Twisted Yangian,JHEP01(2020) 176 [1912.09338]

    2020 arXiv

  16. [21]

    Gombor,On exact overlaps for gl(N) symmetric spin chains,Nucl

    T. Gombor,On exact overlaps for gl(N) symmetric spin chains,Nucl. Phys. B983(2022) 115909 [2110.07960]

    2022 arXiv

  17. [22]

    Gombor,Exact Overlaps for All Integrable Matrix Product States of Rational Spin Chains,Phys

    T. Gombor,Exact Overlaps for All Integrable Matrix Product States of Rational Spin Chains,Phys. Rev. Lett.135(2025) 150402 [2410.23282]

    2025 arXiv

  18. [23]

    Gombor,Derivations for the MPS overlap formulas of rational spin chains,JHEP10 (2025) 035 [2505.20234]

    T. Gombor,Derivations for the MPS overlap formulas of rational spin chains,JHEP10 (2025) 035 [2505.20234]

    2025 arXiv

  19. [24]

    Kristjansen, D.-L

    C. Kristjansen, D.-L. Vu and K. Zarembo,Integrable domain walls in ABJM theory,JHEP 02(2022) 070 [2112.10438]

    2022 arXiv

  20. [25]

    Gombor and C

    T. Gombor and C. Kristjansen,Overlaps for matrix product states of arbitrary bond dimension in ABJM theory,Phys. Lett. B834(2022) 137428 [2207.06866]

    2022 arXiv

  21. [28]

    Bai and M.-Z

    N. Bai and M.-Z. Shao,Integrable matrix product states of ABJM theory from projecting method,Mod. Phys. Lett. A40(2025) 2550068 [2411.09282]

    2025 arXiv

  22. [29]

    Liu and J

    Y. Liu and J. Wu,Chiral integrable boundary states in the SU(4) alternating spin chain,Sci. China Phys. Mech. Astron.69(2026) 231011 [2507.03489]

    2026

  23. [31]

    Minahan, W

    J.A. Minahan, W. Schulgin and K. Zarembo,Two loop integrability for Chern-Simons theories with N=6 supersymmetry,JHEP03(2009) 057 [0901.1142]

    2009 arXiv

  24. [32]

    Bandres, A.E

    M.A. Bandres, A.E. Lipstein and J.H. Schwarz,Studies of the abjm theory in a formulation with manifest su(4) r-symmetry,Journal of High Energy Physics2008(2008) 027–027

    2008

  25. [33]

    de Leeuw, C

    M. de Leeuw, C. Kristjansen and K. Zarembo,One-point Functions in Defect CFT and Integrability,JHEP08(2015) 098 [1506.06958]

    2015 arXiv

  26. [34]

    Buhl-Mortensen, M

    I. Buhl-Mortensen, M. de Leeuw, C. Kristjansen and K. Zarembo,One-point Functions in AdS/dCFT from Matrix Product States,JHEP02(2016) 052 [1512.02532]

    2016 arXiv

  27. [35]

    Gombor and Z

    T. Gombor and Z. Bajnok,Boundary states, overlaps, nesting and bootstrapping AdS/dCFT, JHEP10(2020) 123 [2004.11329]

    2020 arXiv

  28. [36]

    Kristjansen, D

    C. Kristjansen, D. M¨ uller and K. Zarembo,Overlaps and fermionic dualities for integrable super spin chains,JHEP03(2021) 100 [2011.12192]

    2021 arXiv

  29. [37]

    Kristjansen and K

    C. Kristjansen and K. Zarembo,Integrable Holographic Defect CFTs, inGravity, Strings and Fields: A Conference in Honour of Gordon Semenoff, 1, 2024, DOI [2401.17144]. – 28 –

    2024 arXiv

  30. [38]

    Kristjansen, X

    C. Kristjansen, X. Qian and C. Su,The spectrum of defect ABJM theory,JHEP05(2025) 207 [2412.17479]

    2025 arXiv

  31. [39]

    Bianchi,A note on scattering amplitudes on the moduli space of ABJM,JHEP06 (2015) 194 [1502.05352]

    M.S. Bianchi,A note on scattering amplitudes on the moduli space of ABJM,JHEP06 (2015) 194 [1502.05352]

    2015 arXiv

  32. [40]

    Buhl-Mortensen, M

    I. Buhl-Mortensen, M. de Leeuw, A.C. Ipsen, C. Kristjansen and M. Wilhelm,A Quantum Check of AdS/dCFT,JHEP01(2017) 098 [1611.04603]

    2017 arXiv

  33. [41]

    Gombor and Z

    T. Gombor and Z. Bajnok,Dual overlaps and finite coupling ’t Hooft loops,JHEP12(2024) 034 [2408.14901]

    2024 arXiv

  34. [42]

    Kristjansen and K

    C. Kristjansen and K. Zarembo,’t Hooft loops and integrability,JHEP08(2023) 184 [2305.03649]

    2023 arXiv

  35. [43]

    Gromov and P

    N. Gromov and P. Vieira,The all loop AdS4/CFT3 Bethe ansatz,JHEP01(2009) 016 [0807.0777]

    2009 arXiv

  36. [44]

    Ahn and R.I

    C. Ahn and R.I. Nepomechie,N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations,JHEP09(2008) 010 [0807.1924]

    2008 arXiv

  37. [45]

    Komatsu and Y

    S. Komatsu and Y. Wang,Non-perturbative defect one-point functions in planarN= 4 super-Yang-Mills,Nucl. Phys. B958(2020) 115120 [2004.09514]

    2020 arXiv

  38. [46]

    Gombor and Z

    T. Gombor and Z. Bajnok,Boundary state bootstrap and asymptotic overlaps in AdS/dCFT, JHEP03(2021) 222 [2006.16151]

    2021 arXiv

  39. [47]

    Drukker and D

    N. Drukker and D. Trancanelli,A Supermatrix model for N=6 super Chern-Simons-matter theory,JHEP02(2010) 058 [0912.3006]

    2010 arXiv

  40. [48]

    Drukker and Z

    N. Drukker and Z. Kong,1/3 BPS loops and defect CFTs in ABJM theory,JHEP06(2023) 137 [2212.03886]

    2023 arXiv

  41. [49]

    Drukker, J

    N. Drukker, J. Plefka and D. Young,Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals,JHEP11(2008) 019 [0809.2787]

    2008 arXiv

  42. [50]

    Chen and J.-B

    B. Chen and J.-B. Wu,Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory,Nucl. Phys. B825(2010) 38 [0809.2863]

    2010 arXiv

  43. [51]

    S.-J. Rey, T. Suyama and S. Yamaguchi,Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual,JHEP03(2009) 127 [0809.3786]

    2009 arXiv

  44. [52]

    Ouyang, J.-B

    H. Ouyang, J.-B. Wu and J.-j. Zhang,Novel BPS Wilson loops in three-dimensional quiver Chern–Simons-matter theories,Phys. Lett. B753(2016) 215 [1510.05475]

    2016 arXiv

  45. [53]

    Ouyang, J.-B

    H. Ouyang, J.-B. Wu and J.-j. Zhang,Construction and classification of novel BPS Wilson loops in quiver Chern–Simons-matter theories,Nucl. Phys. B910(2016) 496 [1511.02967]

    2016 arXiv

  46. [54]

    Mauri, H

    A. Mauri, H. Ouyang, S. Penati, J.-B. Wu and J. Zhang,BPS Wilson loops inN ≥2 superconformal Chern-Simons-matter theories,JHEP11(2018) 145 [1808.01397]

    2018 arXiv

  47. [55]

    Drukker et al.,Roadmap on Wilson loops in 3d Chern–Simons-matter theories,J

    N. Drukker et al.,Roadmap on Wilson loops in 3d Chern–Simons-matter theories,J. Phys. A 53(2020) 173001 [1910.00588]

    2020 arXiv

  48. [56]

    Kapustin, B

    A. Kapustin, B. Willett and I. Yaakov,Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter,JHEP03(2010) 089 [0909.4559]

    2010 arXiv

  49. [57]

    Marino and P

    M. Marino and P. Putrov,ABJM theory as a Fermi gas,J. Stat. Mech.1203(2012) P03001 [1110.4066]. – 29 –

    2012 arXiv

  50. [58]

    Drukker, M

    N. Drukker, M. Marino and P. Putrov,From weak to strong coupling in ABJM theory, Commun. Math. Phys.306(2011) 511 [1007.3837]

    2011 arXiv

  51. [59]

    de Leeuw, C

    M. de Leeuw, C. Kristjansen and S. Mori,AdS/dCFT one-point functions of the SU(3) sector,Phys. Lett. B763(2016) 197 [1607.03123]

    2016 arXiv

  52. [60]

    Kristjansen, D

    C. Kristjansen, D. M¨ uller and K. Zarembo,Duality relations for overlaps of integrable boundary states in AdS/dCFT,JHEP09(2021) 004 [2106.08116]

    2021 arXiv

  53. [61]

    Buhl-Mortensen, M

    I. Buhl-Mortensen, M. de Leeuw, A.C. Ipsen, C. Kristjansen and M. Wilhelm,One-loop one-point functions in gauge-gravity dualities with defects,Phys. Rev. Lett.117(2016) 231603 [1606.01886]. – 30 –

    2016 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.