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Poisson-Lie duals of the η deformed symmetric space sigma model

Poisson-Lie duals of the \(\eta\) deformed symmetric space sigma model
Authors: Ben Hoare; Fiona K. Seibold;

Poisson-Lie duals of the η deformed symmetric space sigma model

Abstract

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.

Country
Switzerland
Related Organizations
Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
18
Top 10%
Average
Top 10%
Green
Published in a Diamond OA journal