On circular strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$

Abstract

The so called one-parameter (often called $\varkappa$) deformed $AdS$ string sigma models have attracted a lot of attention lately in the study of integrability in string theory. We construct various circular string solutions in the $(Ad{S}_3\times S^3{)}_{\varkappa }$ background and describe the characteristics of such solutions qualitatively. We study the Bohr-Sommerfeld like quantization for these string states to characterise the motion. Further we find a `long' string limit of such circular strings in the $\varkappa$-deformed $Ad{S}_3$ and find a novel dependence of the oscillation number on the energy in the next to leading order expansion.

arXiv commentv2: References added, typos corrected

References in corpus (56)

• The Large N Limit of Superconformal Field Theories and Supergravity
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• A semi-classical limit of the gauge/string correspondence
• The N=4 SYM Integrable Super Spin Chain
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Bethe Ansatz for Quantum Strings
• Classical/quantum integrability in AdS/CFT
• Giant Magnons
• The su(2|2) Dynamic S-Matrix
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• On integrability of the Yang-Baxter $\si$-model
• The Factorized S-Matrix of CFT/AdS
• An integrable deformation of the AdS_5 x S^5 superstring action
• Lax Pair for Strings in Lunin-Maldacena Background
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• Circular Semiclassical String Solutions on AdS_5 x S_5
• On deformations of AdS_n x S^n supercosets
• Integrability of the bi-Yang-Baxter sigma-model
• Spiky strings and single trace operators in gauge theories
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Yang-Mills Duals for Semiclassical Strings
• Integrable Deformations of Strings on Symmetric Spaces
• Strings on Semisymmetric Superspaces
• Green-Schwarz Strings in TsT-transformed backgrounds
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• Supergravity backgrounds for deformations of AdS_n x S^n supercoset string models
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Semiclassical Bethe Ansatz and AdS/CFT
• Double Wick rotating Green-Schwarz strings
• Pulsating Strings on AdS_5 x S^5
• Semi-classical strings in AdS_4*CP^3
• Generalized pulsating strings
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Spinning Pulsating String Solitons in AdS_5 x S^5
• Quantum deformations of the flat space superstring
• Finite Size Giant Magnon
• Deformed Neumann model from spinning strings on (AdS_5 x S^5)_η
• Puzzles of eta-deformed AdS_5 x S^5
• Finite-size giant magnons on η-deformed AdS_5 x S^5
• On the Rotating and Oscillating strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Semiclassical circular strings in AdS_5 and "long" gauge field strength operators
• Pulsating strings in warped AdS_6 x S^4 geometry
• A note on oscillating strings in $Ad{S}_3\times S^3$ with mixed three-form fluxes
• Pulsating strings on $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Pulsating Strings With Angular Momenta
• On the pulsating strings in AdS_5 x T^{1,1}
• Holographic Cusped Wilson loops in $q$-deformed $Ad{S}_5\times S^5$ Spacetime
• Some three-point correlation functions in the eta-deformed AdS_5 x S^5

Cited by in corpus (12)

• Abelian Yang-Baxter Deformations and TsT transformations
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Spinning strings in the $\eta$-deformed Neumann-Rosochatius system
• Integrability of the eta-deformed Neumann-Rosochatius model
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• Multispin magnons on deformed $Ad{S}_3\times S^3$
• Stringy correlations on deformed $Ad{S}_3\times S^3$
• Probing $\eta$ deformed backgrounds with $Dp$ branes
• Pulsating strings in $Sch{r}_5\times T^{1,1}$ background
• Investigating (Non)-Integrability and Pulsating String in D3-Brane Background
• Pulsating strings in I-brane background
• Pulsating string solution and stability in two parameter $\chi$-deformed background