Lax pair for strings in Lunin-Maldacena background

By S. Frolov. 2005

519 citations recorded by the source corpus.

Recently Lunin and Maldacena used an SL(3,) transformation of the AdS5 × S5 background to generate a supergravity solution dual to a so-called β-deformation of = 4 super Yang-Mills theory. We use a T-duality-shift-T-duality (TsT) transformation to obtain the β-deformed background for real β ≡ γ, and show that solutions of string theory equations of motion in this background are in one-to-one correspondence with those in AdS5 × S5 with twisted boundary conditions imposed on the U(1) isometry fields. We then apply the TsT transformation to derive a local and periodic Lax pair for the bosonic part of string theory in the γ-deformed background. We also perform a chain of three consecutive TsT transformations to generate a three-parameter deformation of AdS5 × S5. The three-parameter background is dual to a nonsupersymmetric marginal deformation of = 4 SYM. Finally, we combine the TsT transformations with SL(2,) ones to obtain a 6+2 parameter deformation of AdS5 × S5.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5cee5ed198b231103361423a642d292f152c4989

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Citations in the corpus

Towards integrability for AdS 3 / CFT 2 ?> (2014, background): “This road has been taken in the case of AdS5/CFT4, where a plethora of deformations has been shows to preserve integrability, such as orbifolds [251,252] and T-duality-shift-T-duality (TsT) deformations [253,254] of the background, and quantum deformations (in the sense of quantum groups) of the und”
Green-Schwarz Strings in TsT-transformed backgrounds (2005, methodology): “The observation of [1] can be easily generalized to construct regular multi-parameter deformations of gravity backgrounds if they contain a higher-dimensional torus [2] by using a chain of TsT transformations.”
Gauge-string duality for (non)supersymmetric deformations of N=4 super-Yang–Mills theory (2005, background): “We shall then discuss the BPS states and more general geodesics on γi-deformed S 5 representing semiclassical point-like string states.”
Target space supergeometry of η and λ-deformed strings (2016, background): “The 1These deformations extend to any Z4-symmetric supercoset sigma model, i.e. symmetric space RR string background preserving supersymmetry. 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 respective”
Scattering amplitudes, Wilson loops and the string/gauge theory correspondence (2008, background): “This formulation allows for simple non-supersymmetric generalizations [124].”
Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence (2014, methodology): “3) For the other field components, see [58].”
The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations (2006, methodology): “models [35, 36] which are known to be related to Green-schwarz superstrings in AdS5 × S(5) subject to twisted boundary conditions [36, 34].”
On the rotating and oscillating strings in (AdS3 × S3)ϰ (2014, result): “shown that the string sigma model on AdS5 × S5 admits deformation which preserve the integrability[8]. Typically they are constructed by applying T-duality on any given integrable model(e.g. [9],[10],[11], [12],[13],[14]). Contrary to the usual wisdom, however more recently, a novel example of a one”
S-matrix for strings on η-deformed AdS5 × S5 (2013, background): “J H E P 0 4 ( 2 0 1 4 ) 0 0 2 giving a string theory on a TsT-transformed background [4, 5].”
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].”
Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries (2010, methodology): “Integrability and the LM background Integrability of the IIB Green–Schwarz sigma model in the real-β deformed case was demonstrated in [7] by explicit construction of a Lax pair for the LM background.”
Beauty and the twist: the Bethe ansatz for twisted = 4 SYM (2005, unknown): “ar X iv :h ep -t”
Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory (2005, background): “In present AdS/CFT context, the energy of the corresponding quantum string states will in general involve functions of λ interpolating between the “perturbative string theory” (E = √ λ(E+ b1√ λ + ...)) and the “perturbative gauge theory” (E = c1λ+ c2λ 2 + ...) regimes.”
Abelian Yang–Baxter deformations and TsT transformations (2016, background): “The primary example of this is a string on the Lunin-Maldacena background [5, 6, 7], dual to real β deformed planar SYM.”