Elliptic solutions in the Neumann-Rosochatius system with mixed flux

Abstract

Closed strings spinning in AdS_3 x S^3 x T^4 with mixed R-R and NS-NS three-form fluxes are described by a deformation of the one-dimensional Neumann-Rosochatius integrable system. In this article we find general solutions to this system that can be expressed in terms of elliptic functions. We consider closed strings rotating either in S^3 with two different angular momenta or in AdS_3 with one spin. In order to find the solutions we will need to extend the Uhlenbeck integrals of motion of the Neumann-Rosochatius system to include the contribution from the flux. In the limit of pure NS-NS flux, where the problem can be described by a supersymmetric WZW model, we find exact expressions for the classical energy in terms of the spin and the angular momenta of the spinning string.

18 pages. Latex. v2: Extended discussions, corrected misprints and added reference. Published version

References in corpus (17)

• 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 complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
• Towards integrability for AdS3/CFT2
• Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase
• $Ad{S}_3\times S^3\times M^4$ string S-matrices from unitarity cuts
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Spinning strings and minimal surfaces in $Ad{S}_3$ with mixed 3-form fluxes
• Spinning strings in AdS_3 x S^3 with NS-NS flux
• Macroscopic (and Microscopic) Massless Modes
• One- and two-loop checks for the AdS(3) x S(3) x T(4) superstring with mixed flux
• Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2)
• String solutions in AdS_3 x S^3 x T^4 with NS-NS B-field
• An improved AFS phase for AdS3 string integrability
• String theory in AdS_3 x S^3 x T^4 with mixed flux: semiclassical and 1-loop phase in the S-matrix

Cited by in corpus (3)

• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• Spinning strings in the $\eta$-deformed Neumann-Rosochatius system