Neumann-Rosochatius system for rotating strings in $Ad{S}_3\times S^3\times S^3\times S^1$ with flux

Abstract

Strings on $Ad{S}_3\times S^3\times S^3\times S^1$ with mixed flux exhibit exact integrability. We wish to construct an integrable Neumann-Rosochatius (NR) model of strings starting with the type IIB supergravity action in $Ad{S}_3\times S^3\times S^3\times S^1$ with pure NSNS flux. We observe that the forms of the Lagrangian and the Uhlenbeck integrals of motion of the considered system are NR-like with some suitable deformations which eventually appear due to the presence of flux. We utilize the integrable framework of the deformed NR model to analyze rigidly rotating spiky strings moving only in $S^3\times S^1$. We further present some mathematical speculations on the rounding-off nature of the spike in the presence of non-zero angular momentum $J$ in $S^1$.

24 pages

References in corpus (15)

• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• Spiky strings and giant magnons on S5
• Towards integrability for AdS3/CFT2
• $Ad{S}_3\times S^3\times M^4$ string S-matrices from unitarity cuts
• Solitons and AdS String Solutions
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• Elliptic solutions in the Neumann-Rosochatius system with mixed flux
• Spinning strings in the $\eta$-deformed Neumann-Rosochatius system
• Integrability of the eta-deformed Neumann-Rosochatius model
• Spiky strings in Bethe Ansatz at strong coupling
• Neumann-Rosochatius system for (m,n) string in $Ad{S}_3\times S^3$ with mixed flux
• Double Yang-Baxter deformation of spinning strings
• N spike D-strings in AdS Space with mixed flux
• $N$-spike string in $Ad{S}_3\times S^1$ with mixed flux