Abstract
SL(2,{mathbb {Z}}) invariant action for probe (m, n) string in AdS_3times S^3times T^4 with mixed three-form fluxes can be described by an integrable deformation of an one-dimensional Neumann–Rosochatius (NR) system. We present the deformed features of the integrable model and study general class of rotating and pulsating solutions by solving the integrable equations of motion. For the rotating string, the explicit solutions can be expressed in terms of elliptic functions. We make use of the integrals of motion to find out the scaling relation among conserved charges for the particular case of constant radii solutions. Then we study the closed (m, n) string pulsating in R_ttimes S^3. We find the string profile and calculate the total energy of such pulsating string in terms of oscillation number ({mathcal {N}}) and angular momentum ({mathcal {J}}).
Highlights
These types of string state have not been explored enough as compared to the rigidly rotating strings
The appearance of integrability as a symmetry in Green-Schwarz action of type IIB string in compactified Ad S3 × S3 × M4 background with mixed R–R and NS–NS three form flux has put forth a renewed interest to analyse the Ad S3/C F T2 duality in the presence of mixed fluxes by means of well known classical integrable models
There are several recent works [39,40,41,42,43,44,45] which reveal that general solutions corresponding to closed rotating and pulsating string in various 10D AdS/S compact spaces with pure or mixed flux may be constructed from systematic analysis of the one dimensional Lagrangian of NR system with integrable deformation
Summary
These types of string state have not been explored enough as compared to the rigidly rotating strings. There are several recent works [39,40,41,42,43,44,45] which reveal that general solutions corresponding to closed rotating and pulsating string in various 10D AdS/S compact spaces with pure or mixed flux may be constructed from systematic analysis of the one dimensional Lagrangian of NR system with integrable deformation. A lot of work has been devoted for constructing various string-like as well as five-brane solutions of type IIB supergravity equations using S L(2, Z) invariance of low energy effective action of this theory [46,47,48,49,50,51,52]. For intermediate value of q the theory has not been completely understood till date
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