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Integrable open spin-chains in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>AdS</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>CFT</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>correspondences
We study integrable open boundary conditions for $\mathfrak{d}(2,1;\ensuremath{\alpha}{)}^{2}$ and $\mathfrak{p}\mathfrak{s}\mathfrak{u}(1,1|2{)}^{2}$ spin-chains. Magnon excitations of these open spin-chains are mapped to massive excitations of type-IIB open superstrings ending on D-branes in the ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ and ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{T}^{4}$ supergravity geometries with pure R-R flux. We derive reflection matrix solutions of the boundary Yang-Baxter equation …