Integrable deformations of strings on symmetric spaces

By T. Hollowood, J. Miramontes, David M. Schmidtt. Journal of High Energy Physics, 2014

193 citations recorded by the source corpus.

A general class of deformations of integrable sigma-models with symmetric space F/G target-spaces are found. These deformations involve defining the non-abelian T dual of the sigma-model and then replacing the coupling of the Lagrange multiplier imposing flatness with a gauged F/F WZW model. The original sigma-model is obtained in the limit of large level. The resulting deformed theories are shown to preserve both integrability and the equations-of-motion, but involve a deformation of the symplectic structure. It is shown that this deformed symplectic structure involves a linear combination of the original Poisson bracket and a generalization of the Faddeev-Reshetikhin Poisson bracket which we show can be re-expressed as two decoupled F current algebras. It is then shown that the deformation can be incorporated into the classical model of strings on ℝ×F/G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{R}\times F/G $$\end{document} via a generalization of the Pohlmeyer reduction. In this case, in the limit of large sigma-model coupling it is shown that the theory becomes the relativistic symmetric space sine-Gordon theory. These results point to the existence of a deformation of this kind for the full Green-Schwarz superstring on AdS5 × S5.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/855e7ab9f942f8de8190005a7f106adc334bc48e

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In Geometry and Topology

1. A. Tseytlin
2. G. Arutyunov
3. S. Frolov
4. B. Vicedo
5. B. Hoare
6. R. Borsato
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In Mathematical Physics

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In Nuclear and High Energy Physics

1. A. Tseytlin
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3. G. Arutyunov
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5. B. Hoare
6. N. Beisert
7. S. J. Tongeren
8. R. Borsato

Citations in the corpus

• An integrable deformation of the AdS5 × S5 superstring (2014, methodology): “The discussion generalizes that of [22] that addressed the same question for purely bosonic string theories on symmetric spaces.”
• Target space supergeometry of η and λ-deformed strings (2016, background): “The λ-model was originally proposed by [11] and it extends the case of bosonic cosets [12] (see also [13]).”
• Generalised integrable λ- and η-deformations and their relation (2015, methodology): “For comparison we may note that the η̃ = 0 limit returns to the known isotropic λ-deformation of a symmetric coset for which the Lax connection was given in [10] as”
• On integrable deformations of superstring sigma models related to AdSn×Sn supercosets (2015, methodology): “while the parameter λb of [5] is related to the parameter λ of [6] by λb = λ 2 ,”
• Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles (2015, methodology): “Gauged WZW type deformations were recently generalized to all symmetric space σ-models [17] and to semi-symmetric space σ-models in the case of the AdS S 5 5 × superstring [18].”
• Scale invariance of the η-deformed AdS5 × S5 superstring, T-duality and modified type II equations (2015, methodology): “This might be possible in view of the existence of the λ-model [23] which is classically related to the η-model by the Poisson-Lie duality combined with an analytic continuation of the deformation parameter, and for which there is a candidate supergravity solution [24] (i.”