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General boundary conditions for the sl(N) and sl(M|N) open spin chains

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arxiv math-ph/0406021 v3 pith:YAWM4WNZ submitted 2004-06-11 math-ph hep-thmath.MP

General boundary conditions for the sl(N) and sl(M|N) open spin chains

Daniel Arnaudon (LAPTH) , Jean Avan (LPTM) , Nicolas Crampe (LAPTH) , Anastasia Doikou (LAPTH) , Luc Frappat (LAPTH) , Eric Ragoucy (LAPTH) This is my paper
classification math-ph hep-thmath.MP
keywords solitonboundaryconditionscasechainsequationsgeneralnon-preserving
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Two types of boundary conditions ("soliton preserving" and "soliton non-preserving") are investigated for the sl(n) and sl(m|n) open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe Ansatz equations are derived for each case. The general treatment for non-diagonal reflection matrices associated to "soliton preserving" case is worked out. The connection between the "soliton non-preserving" boundary conditions and the twisted (super) Yangians is also discussed.

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Cited by 2 Pith papers

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

    hep-th 2026-07 accept novelty 6.0

    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.

  2. Chiral Integrable Boundary States of ABJM Spin Chain from Reflection Equations

    hep-th 2026-02 unverdicted novelty 6.0

    A framework is proposed for 2n-site chiral integrable matrix product states in the ABJM spin chain from reflection equations, with exact overlap formulas for four-site states and numerical checks of subspaces.