Spin Chain Overlaps and the Twisted Yangian

Abstract

Using considerations based on the thermodynamical Bethe ansatz as well representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the $SO(6)$ spin chain and matrix product states built from matrices whose commutators generate an irreducible representation of $\mathfrak{so}(5)$. The latter play the role of boundary states in a domain wall version of $\mathcal{N}=4$ SYM theory which has non-vanishing, $SO(5)$ symmetric vacuum expectation values on one side of a co-dimension one wall. This theory, which constitutes a defect CFT, is known to be dual to a D3-D7 probe brane system. We likewise show that the same methodology makes it possible to prove an overlap formula, earlier presented without proof, which is of relevance for the similar D3-D5 probe brane system.

arXiv comment47 pages, misprints corrected

References in corpus (39)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Open and Closed String Interpretation of SUSY CFT's on Branes with Boundaries
• Time evolution of local observables after quenching to an integrable model
• The su(2|2) Dynamic S-Matrix
• Holography and Defect Conformal Field Theories
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• What is an integrable quench?
• Four-Dimensional Superconformal Theories with Interacting Boundaries or Defects
• One-point Functions in Defect CFT and Integrability
• One-point Functions in AdS/dCFT from Matrix Product States
• Non-abelian Brane Intersections
• AdS/dCFT one-point functions of the SU(3) sector
• Transport Properties of Holographic Defects
• Longitudinal 5-branes as 4-spheres in Matrix theory
• Scalar one-point functions and matrix product states of AdS/dCFT
• Quantum spectral curve as a tool for a perturbative quantum field theory
• Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory
• One-loop one-point functions in gauge-gravity dualities with defects
• Asymptotic one-point functions in AdS/dCFT
• Exact solution for the quench dynamics of a nested integrable system
• On the R-matrix realization of Yangians and their representations
• Overlaps of Partial Neel States and Bethe States
• One-point functions in massive integrable QFT with boundaries
• Integrable Matrix Product States from boundary integrability
• Finite-dimensional irreducible representations of twisted Yangians
• A Quantum Check of AdS/dCFT
• Expectation values of chiral primary operators in holographic interface CFT
• Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations
• Overlaps with arbitrary two-site states in the XXZ spin chain
• Chiral primary one-point functions in the D3-D7 defect conformal field theory
• Integrable quenches in nested spin chains I: the exact steady states
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
• Twisted Yangians for symmetric pairs of types B, C, D
• Representations of twisted Yangians of types B, C, D: I
• Nonstandard Bethe Ansatz equations for open O(N) spin chains
• A non-integrable quench from AdS/dCFT
• Representations of twisted Yangians of types B, C, D: II

Cited by in corpus (30)

• Roadmap on Atomtronics: State of the art and perspective
• Entanglement spreading in non-equilibrium integrable systems
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• Boundary states, overlaps, nesting and bootstrapping AdS/dCFT
• Boundary state bootstrap and asymptotic overlaps in AdS/dCFT
• On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
• Integrable domain walls in ABJM theory
• Crosscap States in Integrable Field Theories and Spin Chains
• On exact overlaps in integrable spin chains
• Integrable quenches in the Hubbard model
• On exact overlaps for $\mathfrak{gl}(N)$ symmetric spin chains
• Overlaps for Matrix Product States of Arbitrary Bond Dimension in ABJM theory
• Solution of the BEC to BCS Quench in One Dimension
• Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
• String integrability of the ABJM defect
• Wrapping corrections for long range spin chains
• Holographic correlators of semiclassical states in defect CFTs
• Exact Overlaps in the Lieb-Liniger Model from Coordinate Bethe Ansatz
• More on Affine Dynkin Quiver Yangians
• Integrable crosscaps in classical sigma models
• B-type anomaly coefficients for the D3-D5 domain wall
• Holography of a novel codimension-2 defect CFT
• TCSA and the finite volume boundary state
• Wilson loops correlators in defect $\mathcal{N}=4$ SYM
• Three-Point Functions in ABJM and Bethe Ansatz
• B-type anomaly coefficients for the D3-D7 domain wall
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM
• SO(n) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(n) spin chains
• On computing non-equilibrium dynamics following a quench
• Chiral Integrable Boundary States in the SU(4) Alternating Spin Chain