Abstract
We present a general formalism to investigate the integrable properties of a large class of non-ultralocal models which in principle allows the construction of the corresponding lattice versions. Our main motivation comes from the subsector of the string theory on AdS5 × S5 in the uniform gauge, where such type of non-ultralocality appears in the resulting Alday–Arutyunov–Frolov (AAF) model. We first show how to account for the second derivative of the delta function in the Lax algebra of the AAF model by modifying Maillet’s r- and s-matrices formalism, and derive a well-defined algebra of transition matrices, which allows for the lattice formulation of the theory. We illustrate our formalism on the examples of the bosonic Wadati–Konno–Ichikawa–Shimizu (WKIS) model and the two-dimensional free massive Dirac fermion model, which can be obtained by a consistent reduction of the full AAF model, and give the explicit forms of their corresponding r-matrices.
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