Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit

Abstract

In this article we construct the effective field theory associated to the $\mathbb{R}\times S^3$ sector of the three-parameter deformation of $Ad{S}_3\times S^3\times T^4$ in the Landau-Lifshitz approximation. We use this action to compute the dispersion relation of excitations around the BMN vacuum and the perturbative $S$-matrix associated to them. We are able to compute and sum all the different loop contributions to the $S$-matrix in this limit.

arXiv comment19 pages, 1 figure. v2: References added. v3: References added, typos corrected. Published version

References in corpus (64)

• Review of AdS/CFT Integrability: An Overview
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• On integrability of the Yang-Baxter $\si$-model
• Foundations of the AdS_5 x S^5 Superstring. Part I
• An integrable deformation of the AdS_5 x S^5 superstring action
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Spin chains and string theory
• On classical q-deformations of integrable sigma-models
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Integrability and the AdS(3)/CFT(2) correspondence
• Jordanian deformations of the AdS_5xS^5 superstring
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• On deformations of AdS_n x S^n supercosets
• Integrability of the bi-Yang-Baxter sigma-model
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• The SU(3) spin chain sigma model and string theory
• Strings on NS-NS Backgrounds as Integrable Deformations
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix
• Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux
• Integrable deformations of T-dual $\sigma$ models
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Supergravity backgrounds for deformations of AdS_n x S^n supercoset string models
• Integrable double deformation of the principal chiral model
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• Towards integrability for AdS3/CFT2
• A Jordanian deformation of AdS space in type IIB supergravity
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Bethe Ansatz in Stringy Sigma Models
• Integrable spin chain for stringy Wess-Zumino-Witten models
• SL(2) spin chain and spinning strings on AdS_5xS^5
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
• Schrödinger geometries arising from Yang-Baxter deformations
• On non-abelian T-duality and deformations of supercoset string sigma-models
• Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x S5 superstrings
• Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
• Spin chain sigma models with fermions
• 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
• Super spin chain coherent state actions and $Ad{S}_5\times S^5$ superstring
• Integrable deformations of the AdS${}_5\times$S${}^5$ superstring and the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence --
• On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring
• Spinning strings in AdS_3 x S^3 with NS-NS flux
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• 1/J^2 corrections to BMN energies from the quantum long range Landau-Lifshitz model
• The Effectiveness of Relativistic Invariance in AdS${}_3$
• Two-parameter integrable deformations of the $Ad{S}_3\times S^3\times T^4$ superstring
• Unimodular jordanian deformations of integrable superstrings
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
• Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions
• Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
• Yangian Symmetry of String Theory on $Ad{S}_3\times S^3\times S^3\times S^1$ with Mixed 3-form Flux
• Superstring sigma models from spin chains: the SU(1,1|1) case
• Three-parameter integrable deformation of Z_4 permutation supercosets
• Sigma model from SU(1,1|2) spin chain
• On S-Matrix factorization of the Landau-Lifshitz model
• Fast spinning strings on $\eta$ deformed $Ad{S}_5\times S^5$
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• Spin chains and classical strings in two parameters $q$-deformed AdS${}_3\times$S${}^3$
• The $\mathrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten spin-chain $\sigma$-model
• The $SU(2)$ Wess-Zumino-Witten spin chain sigma model

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• A study of integrable form factors in massless relativistic AdS_3
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• Pulsating string solution and stability in two parameter $\chi$-deformed background