Abstract
We formulate and close the boundary state bootstrap for factorizing K-matrices in AdS/CFT. We found that there are no boundary degrees of freedom in the boundary bound states, merely the boundary parameters are shifted. We use this family of boundary bound states to describe the D3-D5 system for higher dimensional matrix product states and provide their asymptotic overlap formulas. In doing so we generalize the nesting for overlaps of matrix product states and Bethe states.
Highlights
Integrable boundary states can be equivalently described by the K-matrix, which encodes how pairs of particles are annihilated
If the theory and the mirror theory is not equivalent, as in the AdS/CFT correspondence, the boundary bootstrap for the reflection factor is not equivalent to the boundary bootstrap for the boundary state. This boundary state bootstrap, which is equivalent to the boundary bootstrap for the mirror reflection factor, can be formulated more intuitively in the original theory
In [18] we developed a nesting method to calculate the K-matrices of the excitations in nested Bethe Ansatz systems and analyzed the cases when the matrix product states were in the two dimensional representations of su(2)
Summary
Of the KYBE without inner degrees of freedom [18] We found that they all have centrally extended osp(2|2)c residual symmetry and the various solutions were characterized by how this symmetry can be embedded into the centrally extended su(2|2)c. Where x± ≡ x±(p) are the standard parameters of the one-particle representations This parametrization is slightly different from [18] by rescaling ki, which parameterize the orientation of the bosonic part of the osp(2|2)c ⊂ su(2|2)c embedding, while the parameter xs is responsible for the fermionic orientation Qαa = Qαa + ix−s 1 αβσ1abQ†b β, with σ1 being the first Pauli matrix. Unitarity of the mirror reflection factor implies the following equation for the scalar factor. The poles signal boundary bound states and in the following we calculate the K-matrices of the corresponding excited boundary state
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