On RG flow and dual description of N=2 supersymmetric 2d integrable sigma models

Abstract: There are several known examples of integrable deformations of 2D sigma models, including N=2 supersymmetric ones, for which there exist dual descriptions in terms of Toda-type theories. For such deformations there is a system of screening charges, depending on the continuous parameter b, which determines deformed sigma model in the limit b to infinity and certain quantum field theory of Toda type in the limit b to 0. In the latter regime one can see that the 2-particle scattering matrix coincides with the expansion of the trigonometric S-matrix of the corresponding deformed sigma model. In the sigma model regime it can be shown that the leading ultraviolet asymptotic of the deformed sigma model coincides with perturbed Gaussian theory. We study the regularization scheme dependence of Kaehler (N = 2) supersymmetric sigma models. At the one-loop order the metric beta-function is the same as in the non-supersymmetric case and it coincides with the Ricci tensor. The first correction in the MS scheme is known to appear in the fourth loop in both cases. Also for the N=2 case the fifth loop contribution was previously calculated. We show that for certain integrable Kähler backgrounds, such as the complete T-dual of eta-deformed CP(n) sigma models and lambda-deformed ones, there is a renormalization scheme in which the fourth and fifth loop contributions vanish. This potentially paves the way for the all-loop dual description of such sigma models in terms of Toda type theories.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( slides | video )

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BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

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