On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain

Abstract

We study the link between WZW model and the spin-1/2 XYZ chain. This is achieved by comparing the second-order differential equations from them. In the former case, the equation is the Ward-Takahashi identity satisfied by one-point toric conformal blocks. In the latter case, it arises from Baxter's TQ relation. We find that the dimension of the representation space w.r.t. the V-valued primary field in these conformal blocks gets mapped to the total number of chain sites. By doing so, Stroganov's "The Importance of being Odd" (cond-mat/0012035) can be consistently understood in terms of WZW model language. We first confirm this correspondence by taking a trigonometric limit of the XYZ chain. That eigenstates of the resultant two-body Sutherland model from Baxter's TQ relation can be obtained by deforming toric conformal blocks supports our proposal.

17 pages, 3 figures; v2: minor revision; v3: typos in equations corrected

References in corpus (7)

• Darboux coordinates, Yang-Yang functional, and gauge theory
• Deforming SW curve
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Quantization of Integrable Systems and a 2d/4d Duality
• Nekrasov prepotential with fundamental matter from the quantum spin chain
• Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants
• Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and Ω-deformed Seiberg-Witten prepotential