Abstract We study the Gauge/Bethe correspondence for two-dimensional N $$ mathcal{N} $$ = (2, 2) supersymmetric quiver gauge theories associated with toric Calabi-Yau three-folds, whose BPS algebras have recently been identified as the quiver Yangians.We start with the crystal representations of the quiver Yangian, which are placed at each site of the spin chain.We then construct integrable models by combining the single-site crystals into Study on Illumination Intensity and Duration of LED Light Sources for a Weaned Piglet House without Natural Light crystal chains by a coproduct of the algebra, which we determine by a combination of representation-theoretical and gauge-theoretical arguments.For non-chiral quivers, we find that the Bethe ansatz equations for the crystal chain coincide with the vacuum equation of the quiver gauge theory, thus confirming the corresponding Gauge/Bethe correspondence.For more general chiral quivers, however, we find obstructions to the R-matrices satisfying the Yang-Baxter equations and the unitarity conditions, and hence to their corresponding Gauge/Bethe correspondence.
We also discuss trigonometric (quantum toroidal) versions of the quiver BPS Enrichment of ruminant meats with health enhancing fatty acids and antioxidants: feed-based effects on nutritional value and human health aspects – invited review algebras, which correspond to three-dimensional N $$ mathcal{N} $$ = 2 gauge theories and arrive at similar conclusions.Our findings demonstrate that there are important subtleties in the Gauge/Bethe correspondence, often overlooked in the literature.