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Register a new userNeumann-Rosochatius system for (m,n) string in $AdS_3 times S^3$ with mixed flux
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$SL(2,mathbb{Z})$ 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 $(cal{N})$ and angular momentum $(cal{J})$.
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Sigma model in $AdS_3times S^3$ background supported by both NS-NS and R-R fluxes is one of the most distinguished integrable models. We study a class of classical string solutions for $N$-spike strings moving in $AdS_3 times S^1$ with angular momentum $J$ in $S^1 subset S^5$ in the presence of mixed flux. We observe that the addition of angular momentum $J$ or winding number $m$ results in the spikes getting rounded off and not end in cusp. The presence of flux shows no alteration to the rounding-off nature of the spikes. We also consider the large $N$-limit of $N$-spike string in $AdS_3 times S^1$ in the presence of flux and show that the so-called Energy-Spin dispersion relation is analogous to the solution we get for the periodic-spike in $AdS_3-pp-$wave $times S^1$ background with flux.
We address the question about the exact form of the dispersion relation for light-cone string excitations in string theory in AdS3 x S3 x T4 with mixed R-R and NS-NS 3-form fluxes. The analogy with string theory in AdS5 x S5 suggests that in addition to the data provided by the perturbative near-BMN expansion and the symmetry algebra considerations there is also another source of information about the dispersion relation -- the semiclassical giant magnon solution. In earlier work in arXiv:1303.1037 and arXiv:1304.4099 it was found that the symmetry algebra constraints consistent with perturbative expansion do not completely determine the form of the dispersion relation. The aim of the present paper is to fix it by constructing a generalization of the known dyonic giant magnon soliton on S3 to the presence of a non-zero NS-NS flux described by a WZ term in the string action. We find that the angular momentum of this soliton gets shifted by a term linear in world-sheet momentum. We also discuss the symmetry algebra of the string light-cone S-matrix and show that the exact dispersion relation, which should have the correct perturbative BMN and semiclassical giant magnon limits, should also contain such a linear momentum term. The simplicity of the resulting bound-state picture provides a strong argument in favour of this dispersion relation.
We study the finite size effect of rigidly rotating strings and closed folded strings in $AdS_3times S^3$ geometry with NS-NS B-field. We calculate the classical exponential corrections to the dispersion relation of infinite size giant magnon and single spike in terms of Lambert $mathbf{W}-$function. We also write the analytic expression for the dispersion relation of finite size Gubser-Klebanov-Polyakov (GKP) string in the form of Lambert $mathbf{W}-$function.
Neumann-Rosochatius system is a well known one dimensional integrable system. We study the rotating and pulsating string in $AdS_4 times mathbb{CP}^3$ with a $B_{rm{NS}}$ holonomy turned on over $mathbb{CP}^1 subset mathbb{CP}^3$, or the so called Aharony-Bergman-Jafferis (ABJ) background. We observe that the string equations of motion in both cases are integrable and the Lagrangians reduce to a form similar to that of deformed Neuman-Rosochatius system. We find out the scaling relations among various conserved charges and comment on the finite size effect for the dyonic giant magnons on $R_{t}times mathbb{CP}^{3}$ with two angular momenta. For the pulsating string we derive the energy as function of oscillation number and angular momenta along $mathbb{CP}^{3}$.
The type IIB supergravity AdS_3 x S^3 x T^4 background with mixed RR and NSNS 3-form fluxes is a near-horizon limit of a non-threshold bound state of D5-D1 and NS5-NS1 branes. The corresponding superstring world-sheet theory is expected to be integrable, opening the possibility of computing its exact spectrum for any values of the coefficient q of the NSNS flux and the string tension. In arXiv:1303.1447 we have found the tree-level S-matrix for the massive BMN excitations in this theory, which turned out to have a simple dependence on q. Here, by analyzing the constraints of symmetry and integrability, we propose an exact massive-sector dispersion relation and the exact S-matrix for this world-sheet theory. The S-matrix generalizes its recent construction in the q=0 case in arXiv:1303.5995.
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