Abstract
The D3-D5 probe-brane system is holographically dual to a defect CFT which is known to be integrable. The evidence comes mainly from the study of correlation functions at weak coupling. In the present work we shed light on the emergence of integrability on the string theory side. We do so by constructing the double row transfer matrix which is conserved when the appropriate boundary conditions are imposed. The corresponding reflection matrix turns out to be dynamical and depends both on the spectral parameter and the string embedding coordinates.
Highlights
Where λ is the ’t Hooft coupling and the angle α specifies the inclination of the D5-brane relative to the hyperplane x3 = 0
An elegant classification scheme of integrable boundary conditions has been put forward [4] establishing a one-to-one link between integrable D-branes and Z2 automorphisms of the underlying symmetry algebra
Robin boundary conditions are precisely the ones that describe a string attached to a D-brane with internal magnetic flux
Summary
The spectral parameter-dependent part A(x) of the Lax connection (2.2) takes the following form, in the fixed frame: a gAg−1. The object (2.6) is gauge invariant and its time derivative depends on the matter part of the Lax connection. The double row monodromy matrix takes into account the boundary at σ = 0 It is constructed by folding two monodromy matrices together and connecting them through a reflection matrix:. The reflection matrix U is a constant matrix that depends neither on the spectral parameter x nor on time τ. In this case the integrability condition (2.12). Reduces to jτt U + Ujτ =! jσt U − Ujσ =! 0
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