
arXiv: 1709.01448
handle: 20.500.11850/213308
Abstract Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model. In this paper we investigate when the η deformed model can be dualised with respect to a subgroup G0 of G. Starting from the first-order action on the complexified group and integrating out the degrees of freedom associated to different subalgebras, we find it is possible to dualise when G0 is associated to a sub-Dynkin diagram. Additional U1 factors built from the remaining Cartan generators can also be included. The resulting construction unifies both the Poisson-Lie dual with respect to G and the complete abelian dual of the η deformation in a single framework, with the integrated algebras unimodular in both cases. We speculate that extending these results to the path integral formalism may provide an explanation for why the η deformed AdS5 × S5 superstring is not one-loop Weyl invariant, that is the couplings do not solve the equations of type IIB supergravity, yet its complete abelian dual and the λ deformed model are.
High Energy Physics - Theory, integrable field theories, Sigma models, Field Theories in Lower Dimensions, Path integrals in quantum mechanics, FOS: Physical sciences, Model quantum field theories, Groups and algebras in quantum theory and relations with integrable systems, String and superstring theories in gravitational theory, QC770-798, Supergravity, sigma models, Applications of differential geometry to physics, Field theories in lower dimensions, High Energy Physics - Theory (hep-th), Nuclear and particle physics. Atomic energy. Radioactivity, Sigma models; Field theories in lower dimensions; Integrable field theories, field theories in lower dimensions, Integrable Field Theories, Integrable field theories, path integral, Sigma Models
High Energy Physics - Theory, integrable field theories, Sigma models, Field Theories in Lower Dimensions, Path integrals in quantum mechanics, FOS: Physical sciences, Model quantum field theories, Groups and algebras in quantum theory and relations with integrable systems, String and superstring theories in gravitational theory, QC770-798, Supergravity, sigma models, Applications of differential geometry to physics, Field theories in lower dimensions, High Energy Physics - Theory (hep-th), Nuclear and particle physics. Atomic energy. Radioactivity, Sigma models; Field theories in lower dimensions; Integrable field theories, field theories in lower dimensions, Integrable Field Theories, Integrable field theories, path integral, Sigma Models
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