Coideal Quantum Affine Algebra and Boundary Scattering of the Deformed Hubbard Chain

We consider boundary scattering for a semi-infinite one-dimensional deformed Hubbard chain with boundary conditions of the same type as for the Y=0 giant graviton in the AdS/CFT correspondence. We show that the recently constructed quantum affine algebra of the deformed Hubbard chain has a coideal subalgebra which is consistent with the reflection (boundary Yang-Baxter) equation. We derive the corresponding reflection matrix and furthermore show that the aforementioned algebra in the rational limit specializes to the (generalized) twisted Yangian of the Y=0 giant graviton.Comment: 21 page. v2: minor correction

The Quantum Affine Origin of the AdS/CFT Secret Symmetry

We find a new quantum affine symmetry of the S-matrix of the one-dimensional Hubbard chain. We show that this symmetry originates from the quantum affine superalgebra U_q(gl(2|2)), and in the rational limit exactly reproduces the secret symmetry of the AdS/CFT worldsheet S-matrix.Comment: 22 page

Secret Symmetries in AdS/CFT

We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.Comment: 20 pages, pdfLaTeX; Submitted to the Proceedings of the Nordita program `Exact Results in Gauge-String Dualities'; Based on the talk presented by A.T., Nordita, 15 February 201

Reflection algebra, Yangian symmetry and bound-states in AdS/CFT

We present the `Heisenberg picture' of the reflection algebra by explicitly constructing the boundary Yangian symmetry of an AdS/CFT superstring which ends on a boundary with non-trivial degrees of freedom and which preserves the full bulk Lie symmetry algebra. We also consider the spectrum of bulk and boundary states and some automorphisms of the underlying algebras.Comment: 31 page, 8 figures. Updated versio

The Bound State S-matrix of the Deformed Hubbard Chain

In this work we use the q-oscillator formalism to construct the atypical (short) supersymmetric representations of the centrally extended Uq (su(2|2)) algebra. We then determine the S-matrix describing the scattering of arbitrary bound states. The crucial ingredient in this derivation is the affine extension of the aforementioned algebra.Comment: 44 pages, 3 figures. v2: minor correction

Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane

We consider the worldsheet boundary scattering and the corresponding boundary algebras for the Z=0 giant graviton and the Z=0 D7-brane in the AdS/CFT correspondence. We consider two approaches to the boundary scattering, the usual one governed by the (generalized) twisted Yangians and the q-deformed model of these boundaries governed by the quantum affine coideal subalgebras. We show that the q-deformed approach leads to boundary algebras that are of a more compact form than the corresponding twisted Yangians, and thus are favourable to use for explicit calculations. We obtain the q-deformed reflection matrices for both boundaries which in the q->1 limit specialize to the ones obtained using twisted Yangians.Comment: 36 pages. v2: minor typos corrected, references updated; v3: published versio