New Integrable Models from the Gauge/YBE Correspondence

作者：Yamazaki Masahito^*

来源：Journal of Statistical Physics, 2014, 154(3): 895-911.

DOI：10.1007/s10955-013-0884-8

• Yang-Baxter equation
• Exactly solvable models
• Supersymmetric gauge theories

We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d index of a large class of SU(N) quiver gauge theories with the partition function of 2d classical integrable spin models. The integrability of the model (star-star relation) is equivalent with the invariance of the index under the Seiberg duality. Our solution to the Yang-Baxter equation is one of the most general known in the literature, and reproduces a number of known integrable models. Our analysis identifies the Yang-Baxter equation with a particular duality (called the Yang-Baxter duality) between two 4d supersymmetric quiver gauge theories. This suggests that the integrability goes beyond 4d lens indices and can be extended to the full physical equivalence among the IR fixed points.

• 出版日期2014-2