Integrability of Limit Shapes of the Six Vertex Model

Nicolai Reshetikhin, Ananth Sridhar

Published 2015-10-05Version 1

The main result of this paper is the construction of infinitely many conserved quantities (corresponding to commuting transfer-matrices) for the limit shape equation for the 6-vertex model on a cylinder. This suggests that the limit shape equation is an integrable PDE with gradient constraints. At the free fermionic point this equation becomes the complex Burgers equation.