On the classical equivalence of monodromy matrices in squashed sigma model

Abstract

Abstract:We proceed to study the hybrid integrable structure in two-dimensional non-linear sigma models with target space three-dimensional squashed spheres. A quantum affine algebra and a pair of Yangian algebras are realized in the sigma models and, according to them, there are two descriptions to describe the classical dynamics 1) the trigonometric description and 2) the rational description, respectively. For every description, a Lax pair is constructed and the associated monodromy matrix is also constructed. In this paper we show the gauge-equivalence of the monodromy matrices in the trigonometric and rational description under a certain relation between spectral parameters and the rescalings of sl(2) generators.

S-matrix for strings on η-deformed AdS5 × S5

“…Deformations of this type constitute a general class of deformations governed by solutions of the classical Yang-Baxter equation [16,17]. This class is not solely restricted to the string model in question but can be applied to a large variety of two-dimensional integrable models based on (super)groups or their cosets [18]- [21].…”

Yang-Baxter deformations of Minkowski spacetime

“…Deformations of S 3 and AdS 3 have been well investigated [8][9][10][11][12][13][14][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. 1 A systematic way is the Yang-Baxter sigma model approach proposed by Klimcik [11][12][13].…”

Anisotropic Landau-Lifshitz sigma models from q-deformed AdS5×S5 superstrings

“…The remaining task is to check a classical analogue of q-Serre relations, which are deduced by introducing the classical q-Poisson bracket [29,30],…”

“…This algebra can be interpreted as the remnant of the relativistic case [29,30] after taking the fast-moving string limit, while the left Yangians are not realized any more.…”

“…Deformed target spaces are not represented by symmetric cosets, but typically by non-symmetric cosets (For arguments on some examples, see [23]). A particularly simple and tractable example is squashed S 3 and its integrable structure has been studied intensively [24][25][26][27][28][29][30][31][32][33][34][35][36]. In the recent, a generalization to higher dimensions has succeeded for arbitrary compact Lie groups and symmetric cosets [37], by following the Yang-Baxter sigma model description [38][39][40][41].…”