Quantum-group-invariant D n + 1 2 models: Bethe ansatz and finite-size spectrum

Journal article

We consider the quantum integrable spin chain models associated with the Jimbo R-matrix based on the quantum affine algebra Dn+12, subject to quantum-group-invariant boundary conditions parameterized by two discrete variables p = 0, . . . , n and ε = 0, 1. We develop the analytical Bethe ansatz for the previously unexplored case ε = 1 with any n, and use it to investigate the effects of different boundary conditions on the finite-size spectrum of the quantum spin chain based on the rank-2 algebra D32. Previous work on this model with periodic boundary conditions has shown that it is critical for the range of anisotropy parameters 0 < γ < π/4, where its scaling limit is described by a non-compact CFT with continuous degrees of freedom related to two copies of the 2D black hole sigma model. The scaling limit of the model with quantum-group-invariant boundary conditions depends on the parameter ε: similarly as in the rank-1 D22 chain, we find that the symmetry of the lattice model is spontaneously broken, and the spectrum of conformal weights has both discrete and continuous components, for ε = 1. For p = 1, the latter coincides with that of the D22 chain, which should correspond to a non-compact brane related to one black hole CFT in the presence of boundaries. For ε = 0, the spectrum of conformal weights is purely discrete.

Authors: Frahm, H; Gehrmann, S; Nepomechie, RI; Retore, AL

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of High Energy Physics
• Volume: 2025
• Issue: 12
• Article number: 117
• Publication date: 2025-12-16
• Acceptance date: 2025-11-06
• DOI: 10.1007/jhep12(2025)117
• EISSN: 1029-8479
• ISSN: 1126-6708
• Language: English
• Keywords: Bethe Ansatz; Lattice Integrable Models; Sigma Models; Boundary Quantum Field Theory