On integrable boundaries in the 2 dimensional O(N) σ-models

Integrable boundary states can be built up from pair annihilation amplitudes called K-matrices. These amplitudes are related to mirror reflections and they both satisfy Yang Baxter equations, which can be twisted or untwisted. We relate these two notions to each other and show how they are fixed by the unbroken symmetries, which, together with the full symmetry, must form symmetric pairs. We show that the twisted nature of the K-matrix implies specific selection rules for the overlaps. If the Bethe roots of the same type are paired the overlap is called chiral, otherwise it is achiral and they correspond to untwisted and twisted K-matrices, respectively. We use these findings to develop a nesting procedure for K-matrices, which provides the factorizing overlaps for higher rank algebras automatically. We apply these methods for the calculation of the simplest asymptotic all-loop 1-point functions in AdS/dCFT. In doing so we classify the solutions of the YBE for the K-matrices with centrally extended $$ \mathfrak{su} $$ su (2|2)c symmetry and calculate the generic overlaps in terms of Bethe roots and ratio of Gaudin determinants.

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“…For the so(6) spin chain, there are five types of solutions of the KYBE [29]. They can be classified according to their symmetries.…”

Section: K-matrices In the So(6) Spin Chainmentioning

confidence: 99%

Boundary states, overlaps, nesting and bootstrapping AdS/dCFT

Gombor

Bajnok

2020

J. High Energ. Phys.

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“…We shall see that this quite naturally generalises the gluing conditions used in the case of the WZW model. This approach has its origins in [20,21] and has been used in a variety of contexts including the identification of integrable boundary conditions for strings in bosonic sigma models [22], in Green-Schwarz sigma models [23], 2 for the O(N ) sigma model [25,26], the principal chiral model [27,28], open spin chains (e.g. [29,30] although the literature is vast) and affine Toda field theories [31].…”

Section: Jhep09(2018)015mentioning

confidence: 99%

D-branes in λ-deformations

Driezen

Sevrin

Thompson

2018

J. High Energ. Phys.

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We show that the geometric interpretation of D-branes in WZW models as twisted conjugacy classes persists in the λ-deformed theory. We obtain such configurations by demanding that a monodromy matrix constructed from the Lax connection of the λdeformed theory continues to produce conserved charges in the presence of boundaries. In this way the D-brane configurations obtained correspond to "integrable" boundary configurations. We illustrate this with examples based on SU(2) and SL(2, R), and comment on the relation of these D-branes to both non-Abelian T-duality and Poisson-Lie T-duality. We show that the D2 supported by D0 charge in the λ-deformed theory map, under analytic continuation together with Poisson-Lie T-duality, to D3 branes in the η-deformation of the principal chiral model.

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“…we get the boundary condition (17). This boundary condition was already investigated in [7] and [9]. It was shown that this is a conformal boundary condition for all M ∈ g. Now we have just shown that it has a zero curvature representation too for some special M s which satisfy the conditions (16).…”

Section: Lagrangian and Symmetriesmentioning

confidence: 68%

“…1. Restricted boundary conditions when we restrict the field to a lower dimensional sphere These boundary conditions were investigated in [4,5,6,7,8,9] and was shown that all of them are conformal. What can we say about the quantum integrability of these boundary conditions?…”

Section: Introductionmentioning

confidence: 99%

New boundary monodromy matrices for classical sigma models

Gombor

2020

Nuclear Physics B

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The 2d principal models without boundaries have G×G symmetry. The already known integrable boundaries have either H ×H Hereinafter, we look for consistent solutions for the equation (5). The most obvious ansatz for the reflection matrix is κ(λ) = U where U ∈ G is a constant matrix. Using this ansatz, the equation (5) is equivalent to the following two equations:Clearly, J 0 and J 1 are elements of the eigenspaces of the linear transformation Ad U : g → g with +1 and −1 eigenvalues. These are equivalent to dim(g) boundary conditions if and only if U 2 is proportional to 1. Thus, there is a Z 2 graded decomposition g = h ⊕ f where h and f are the +1 and −1 eigenspaces of the Ad U automorphism of g. Therefore the boundary conditions imply J 0 ∈ h and J 1 ∈ f. These are well known integrable boundary conditions [6]. In the

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On integrable boundaries in the 2 dimensional O(N) σ-models

Cited by 13 publications

References 31 publications

Boundary states, overlaps, nesting and bootstrapping AdS/dCFT

Boundary states, overlaps, nesting and bootstrapping AdS/dCFT

D-branes in λ-deformations

New boundary monodromy matrices for classical sigma models

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