Integrable theories and generalized graded Maillet algebras

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 su(1|1) subsector of the string theory on AdS_5 x S^5 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.

37 pages. v2: replaced with published version

References in corpus (7)

• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure
• Alleviating the non-ultralocality of the AdS_5 x S^5 superstring
• First-principles derivation of the AdS/CFT Y-systems
• The r-matrix of the Alday-Arutyunov-Frolov model
• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators

Cited by in corpus (6)

• On the quantization of continuous non-ultralocal integrable systems
• On the equivalence theorem for integrable systems
• The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator
• The tetrahedral Zamolodchikov algebra for the fermionic Bazhanov-Stroganov R-operator
• Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models
• On extension of the Yang-Baxter equation and the fermionic $R$-operator