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On exact overlaps for $\mathfrak{gl}(N)$ symmetric spin chains

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arxiv 2110.07960 v3 pith:X4ONZOK6 submitted 2021-10-15 hep-th math-phmath.MPnlin.SI

Tamás Gombor This is my paper · ORCID
classification hep-thmath-phmath.MPnlin.SI
keywords integrableoverlapsstatesmathfrakoverlapderivationexactfactorized
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abstract

We study the integrable two-site states of the quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(N)$-invariant R-matrix. We investigate the overlaps between the integrable two-site states and the wave-functions. To find exact derivations for the factorized overlap formulas for the nested integrable systems is a longstanding unsolved problem. In this paper we give a derivation for a large class of the integrable states of the $\mathfrak{gl}(N)$ symmetric spin chain. The first part of the derivation is to calculate recurrence relations for the off-shell overlap that uniquely fix it. Using these recursions we prove that the normalized overlaps of the multi-particle states have factorized forms which contain the products of the one-particle overlaps and the ratio of the Gaudin-like determinants. We also show that the previously proposed overlap formulas agree with our general formula.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Derivations for the MPS overlap formulas of rational spin chains

    hep-th 2025-05 conditional novelty 7.0 of 10

    A universal, representation-independent MPS overlap formula is proved for glN rational spin chains and proposed for soN and spN chains.

  2. The spectrum of defect ABJM theory

    hep-th 2024-12 conditional novelty 7.0 of 10

    The quantum fluctuation spectrum of the 1/2-BPS ABJM domain wall is diagonalized and shown to organize into supersymmetric multiplets with conformal dimensions differing by 1/2.

  3. Exact g-function without strings

    hep-th 2024-12 conditional novelty 7.0 of 10

    The exact g-function of sine-Gordon theory with non-diagonal scattering is computed for the first time using lattice regularization and Bethe ansatz.

  4. Monodromy defects in ABJM theory and integrability

    hep-th 2026-08 conditional novelty 6.0 of 10

    Monodromy defects in ABJM theory are integrable boundary states, and their leading one-point functions are given by a closed overlap formula.

  5. Solving for the integrable boundary states of the ABJM spin chain from $KT$-relations

    hep-th 2026-07 accept novelty 6.0 of 10

    Integrable chiral and achiral n-site boundary states of the ABJM spin chain are obtained by solving KT-relations for elementary blocks and K(u), with nontrivial solutions for even n and operator-valued 1-site Clifford pairs.

  6. Integrable matrix product state of ABJM theory from projecting method

    hep-th 2024-11 conditional novelty 6.0 of 10

    This paper classifies projected K-matrix solutions and uses them to propose integrable matrix product states for the ABJM spin chain.

  7. String theory methods for defect CFTs

    hep-th 2025-01 conditional novelty 2.0 of 10

    A review paper that re-presents earlier results on integrable probe-brane defects and holographic defect correlators without adding a new central result.

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