1307.2831 (A. Melikyan et al.)

Integrable theories and generalized graded Maillet algebras    [PDF]

A. Melikyan, G. Weber

We present a general formalism to deal with a large class of graded non-ultralocal models, and investigate their integrable properties. Our main motivation comes from the su(1,1) subsector of the string theory on AdS_5 x S^5 in the uniform gauge, where such severe 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. 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. We also make the first step in establishing a connection between the su(1,1) sub-sector of the strings in the uniform, and in the uniform light cone gauges.

View original: http://arxiv.org/abs/1307.2831