Multi-spike strings in $AdS_3$ with mixed three-form fluxes

On N-spike strings in conformal gauge with NS-NS fluxes

“…This is analogous to the result obtained in [58] using a worldsheet transformation on the q = 0 folded string (N = 2) moving in AdS 3 × S 1 . As we mentioned before, in [57] the dispersion relation for the spiky string with fluxes was obtained perturbatively in q, and the small q expansion of the above result agrees with it, providing a validation for us.…”

“…All of it started as the 'Giant Magnon' dispersion relation was proposed in [44], which turned out to have non-periodic contribution in the momentum as the periodicity is explicitly spoiled by the flux. Subsequently finite-gap solutions were proposed in [49,50] and a large class of folded [51], rotating [52,53,54], pulsating [55,56] and GKP-like multi-spike [57,58] strings have been studied in the literature. Also, well known Neumann-Rosochatius dynamical model of strings has been generalised to AdS 3 × S 3 with NS-NS fluxes together with relevant classical solutions [59,60,61] and one-loop quantization [62] being elucidated in a large number of papers.…”

“…Curiously, the solution had some subtleties in imposing closed string boundary condition and it was found that the next to leading order cusp anomalous dimension (upto O(q 2 )) in that case starts with a term containing − q 2 2 (log S) 2 . In the paper [57] the problem was revisited using a N-spike Kruczenski (static gauge) string solution and the dispersion was again calculated perturbatively in q, where the next to leading order correction turns out − q 2 2 log S, at complete odds with [51]. Finally in [58] it was conjectured using a worldsheet transformation between q = 0 and q = 0 strings in AdS 3 × S 1 , that the dispersion relation in the latter case remains the same as in the pure RR case, but the logarithmic divergence is scaled by a factor of 1 − q 2 .…”

N spike D-strings in AdS Space with mixed flux

“…More recently, the AdS 3 ×S 3 background in the presence of both R-R and NS-NS type fluxes (H 3 = dB 2 and F 3 = dC 2 ) has been proved to be integrable [27], [28]. The integrable structure of this theory, including the S-matrix, has been discussed in [29], [30], [31], [32], [33], [34], and a large number of classical string solutions have been extensively studied in [35], [36], [37], [38], [39]. The background solution has been shown to satisfy type IIB supergravity field equations, provided the parameters associated to field strength of NS-NS fluxes (q) and the one associated to the strength of R-R fluxes (say q) are related by the constraint q 2 + q2 = 1.…”

On multi-spin classical strings with NS-NS flux

“…Once the integrability of the background was proved, a modified 'Giant Magnon' dispersion relation was proposed in [34], which turned out to have non-periodic contribution in the momentum. Subsequently finite-gap equations were proposed [44,45] and a large class of folded [46], rotating [47,48], pulsating [49,50] and GKP-like multi-spike [51] strings were studied in an attempt to formalise the AdS/CFT dictionary to have a hint of the relevant operators. In fact the presence of the fluxes seem to have modified scaling relations between conserved charges considerably to the leading order via terms depending on the parameter b.…”