Classifying Nearest-Neighbor Interactions and Deformations of AdS

Area of Science:

• Theoretical Physics
• Mathematical Physics

Background:

• The Yang-Baxter equation is fundamental in quantum integrable systems.
• Regular solutions of the eight-vertex Yang-Baxter equation relate to spin chains with nearest-neighbor interactions.

Purpose of the Study:

• To classify all regular solutions of the eight-vertex Yang-Baxter equation.
• To identify new solutions and their relation to existing models and holographic systems.

Main Methods:

• Classification of regular solutions for the eight-vertex Yang-Baxter equation.
• Analysis of R-matrix forms (difference vs. nondifference).

Main Results:

• Identified a total of four independent regular solutions.
• Two solutions are related to known six- and eight-vertex models (difference form).
• Discovered two novel solutions of nondifference form, encompassing AdS2 and AdS3 integrable model S-matrices.

Conclusions:

• The two new solutions provide a basis for studying integrable deformations of holographic systems.
• This classification advances the understanding of integrable models and their connections to quantum field theory.