TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.14.6.157
TI  - Classical Lie bialgebras for AdS/CFT integrability by contraction and reduction
PY  - 2023/06/15
UR  - https://www.scipost.org/SciPostPhys.14.6.157
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 14
IS  - 6
SP  - 157
A1  - Beisert, Niklas
AU  - Im, Egor
AB  - Integrability of the one-dimensional Hubbard model and of the factorised scattering problem encountered on the worldsheet of AdS strings can be expressed in terms of a peculiar quantum algebra. In this article, we derive the classical limit of these algebraic integrable structures based on established results for the exceptional simple Lie superalgebra $\mathfrak{d}(2,1;\epsilon)$ along with standard $\mathfrak{sl}(2)$ which form supersymmetric isometries on 3D AdS space. The two major steps in this construction consist in the contraction to a 3D Poincaré superalgebra and a certain reduction to a deformation of the $\mathfrak{u}(2|2)$ superalgebra. We apply these steps to the integrable structure and obtain the desired Lie bialgebras with suitable classical r-matrices of rational and trigonometric kind. We illustrate our findings in terms of representations for on-shell fields on AdS and flat space.
ER  -

@Article{10.21468/SciPostPhys.14.6.157,
	title={{Classical Lie bialgebras for AdS/CFT integrability by contraction and reduction}},
	author={Niklas Beisert and Egor Im},
	journal={SciPost Phys.},
	volume={14},
	pages={157},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.14.6.157},
	url={https://scipost.org/10.21468/SciPostPhys.14.6.157},
}