Green-Schwarz Strings in TsT-transformed backgrounds

By L. Alday, G. Arutyunov, S. Frolov. 2005

184 citations recorded by the source corpus.

We consider classical strings propagating in a background generated by a sequence of TsT transformations. We describe a general procedure to derive the Green-Schwarz action for strings. We show that the U(1) isometry variables of the TsT-transformed background are related to the isometry variables of the initial back- ground in a universal way independent of the details of the background. This allows us to prove that strings in the TsT-transformed background are described by the Green-Schwarz action for strings in the initial background subject to twisted bound- ary conditions. Our construction implies that a TsT transformation preserves inte- grability properties of the string sigma model. We discuss in detail type IIB strings propagating in the γi-deformed AdS5×S 5 space-time, find the twisted boundary con- ditions for bosons and fermions, and use them to write down an explicit expression for the monodromy matrix. We also discuss string zero modes whose dynamics is governed by a fermionic generalization of the integrable Neumann model.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/69af5385310eb28f354ac05850a7f69a972f3706

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Citations in the corpus

The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations (2006, methodology): “This should be relevant for the study of γ -deformed models [35, 36] which are known to be related to Green–Schwarz superstrings in AdS5 × S5 subject to twisted boundary conditions [34, 36].”
Superstrings on AdS4 × ℂℙ3 as a coset sigma-model (2008, background): “5) Indeed, as was shown in [32], the sigma model string Lagrangian of the form (2.”
Abelian Yang–Baxter deformations and TsT transformations (2016, methodology): “In the above σ model, however, we consider theories that are equivalent modulo boundary conditions; TsT transformations can be absorbed in twisted boundary conditions [7, 50].”
Semiclassical quantization of spinning strings in AdS4 × ℂℙ3 (2008, methodology): “As was explained in [29], a convenient and compact representation of the sigma model Lagrangian can be constructed in terms of the following matrix G”
The complete worldsheet S matrix of superstrings on AdS3×S3×T4 with mixed three-form flux (2014, background): “This kappa gauge is the so-called BMN light-cone kappa gauge for fermions that are neutral with respect to the two U(1)’s associated to shifts along t and φ [52].”
Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles (2015, methodology): “Therefore using the above canonical transformation we can relate the deformed model back to the undeformed one but with twisted boundary conditions [34].”
Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory (2015, methodology): “The deformation as a nonlocal gauge transformation Any model of the above type is related to the undeformed AdS5 × S5 superstring by a nonlocal gauge transformation, as originally found for the Lunin-Maldacena background [6, 78].”
Finite-size effects from giant magnons (2006, background): “However, it is possible to redefine the fermions and make them neutral, see [47, 50] for details.”
Foundations of the AdS5 × S5 superstring: I (2009, methodology): “For the alternative parametrization of the coset space discussed in appendix 2 we refer to the work [80] and [82].”
Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries (2010, background): “However it can be shown that these γi-deformations preserve integrability: The Lax pair construction goes through in this case as well [7] and in [50] it was argued that the Green–Schwarz action on TsT-deformed backgrounds is the same as the undeformed one, but with twisted boundary conditions.”
Target space supergeometry of η and λ-deformed strings (2016, background): “[62], the pairs of isometries a, b and c, d do not commute with each other.”
On the rotating and oscillating strings in (AdS3 × S3)ϰ (2014, unknown): “to introduce various classes of integrable deformations to the string sigma model on AdS5 × S5. Typically they are constructed by applying T-duality on any given integrable model(e.g. [11],[12],[13], [14],[15],[16]). Contrary to the usual wisdom, however more recently, a novel example of a one-param”
Towards integrability for AdS 3 / CFT 2 ?> (2014, unknown): “[253].”
Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence (2014, background): “It would be interesting to reinterpret this result from the viewpoint of a twisted boundary condition by following [62].”