η and λ deformations as E-models

By C. Klimčík. 2015

138 citations recorded by the source corpus.

Abstract We show that the so-called λ deformed σ-model as well as the η deformed one belong to a class of the E -models introduced in the context of the Poisson–Lie-T-duality. The λ and η theories differ solely by the choice of the Drinfeld double; for the λ model the double is the direct product G × G while for the η model it is the complexified group G C . As a consequence of this picture, we prove for any G that the target space geometries of the λ-model and of the Poisson–Lie T-dual of the η-model are related by a simple analytic continuation.

Subfields: Algebra and Number Theory, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3d577bb8169adbacb05cae666de019308c39efad

How researchers see this paper

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In Algebra and Number Theory

1. S. J. Tongeren
2. B. Hoare
3. G. Arutyunov
4. R. Roiban
5. S. Frolov
6. David Osten
7. L. Wulff
8. R. Borsato

In Mathematical Physics

1. S. Frolov
2. G. Arutyunov
3. R. Roiban
4. S. J. Tongeren
5. B. Hoare
6. David Osten
7. L. Wulff
8. R. Borsato

In Nuclear and High Energy Physics

1. S. Frolov
2. A. Tseytlin
3. G. Arutyunov
4. S. J. Tongeren
5. R. Roiban
6. N. Beisert
7. R. Borsato
8. M. Staudacher

Citations in the corpus

• Abelian Yang–Baxter deformations and TsT transformations (2016, background): “1 These models are related to another type of integrable deformation known as the λ model [12, 13, 14] by analytic continuation and Poisson-Lie duality [15, 16, 17, 18, 19, 20], see also [21].”
• Scale invariance of the η-deformed AdS5 × S5 superstring, T-duality and modified type II equations (2015, background): “26 Thus if the classical Poisson-Lie duality relation [25] between the η-model and λ-model [26, 12] extends to the full quantum level there may be a way to associate a string theory to the ABF background.”
• Target space supergeometry of η and λ-deformed strings (2016, background): “two deformations are closely related; in fact, in both cases the original symmetry algebra gets q-deformed [14, 15] (with q real and root of unity respectively), and the two models are related, at least at the classical level, by the Poisson-Lie T-duality of [16, 17], see [18, 19, 20].”