A quantum affine algebra for the deformed Hubbard chain

Abstract

The integrable structure of the one-dimensional Hubbard model is based on Shastry's R-matrix and the Yangian of a centrally extended sl(2|2) superalgebra. Alcaraz and Bariev have shown that the model admits an integrable deformation whose R-matrix has recently been found. This R-matrix is of trigonometric type and here we derive its underlying exceptional quantum affine algebra. We also show how the algebra reduces to the above-mentioned Yangian and to the conventional quantum affine sl(2|2) algebra in two special limits.

S-matrix for strings on η-deformed AdS5 × S5

“…In the light-cone gauge this symmetry algebra constitutes two copies of the centrally extended Lie superalgebra psu(2|2) with the same central extension for each copy. It appears that this centrally extended psu(2|2), or more precisely its universal enveloping algebra, admits a natural deformation psu q (2|2) in the sense of quantum groups [6,7]. This algebraic structure is the starting point for the construction of a psu q (2|2) ⊕ psu q (2|2)-invariant S-matrix, giving a quantum deformation of the AdS 5 × S 5 world-sheet S-matrix [6,8,9].…”

Anisotropic Landau-Lifshitz sigma models from q-deformed AdS5×S5 superstrings

“…The non-local charges are conserved under this boundary condition (See appendix C). The non-local conserved charges are given by 13) JHEP08 (2014)110 where χ(x) is a non-local field defined as…”

“…There are two approaches to tackle this issue. The one is an algebraic approach based on q-deformations of the worldsheet S-matrix [12][13][14][15][16][17][18][19]. The deformed S-matrices are constructed in a mathematically consistent way.…”

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

“…The parameters t Q and t G in the twist (3.29) are constrained by requiring the twisted central charges 33) to be coreflective. This gives a constraint t Q = t G = g 2 + 1/4.…”

“…A quantum affine algebra Q leading to a q-deformed S-matrix which in the q → 1 limit specializes to the AdS/CFT worldsheet S-matrix was constructed in [33] and the corresponding q-deformed bound-state S-matrices were found in [34]. However, finding fundamental scattering matrices does not require the full quantum affine algebra, thus the fundamental q-deformed S-matrix was found earlier in [35].…”