On the giant magnon and spike solutions for strings onAdS₃×S³

Abstract

We study solutions for rigidly rotating strings on a two sphere. Among them we find two limiting cases that have a particular interest, one is the already known giant magnon and the other we call the single spike solution. The limiting behavior of this last solution is a string infinitely wrapped around the equator. It differs from that solution by the existence of a single spike of height ¯ θ that points toward the north pole. We study its properties and compute its energy E and angular momentum J as a function of ¯ θ. We further generalize the solution by adding one angular momentum to obtain a solution on S 3. We find a spin chain interpretation of these results in terms of free fermions and the Hubbard model but the exact relation with the same models derived from the field theory is not clear.

Integrability and the AdS 3/CFT 2 correspondence

“…By inspecting the symmetries of the giant magnons in AdS 3 × S 3 [57] and drawing some intuition from the spin chain picture in the dual CFT, David and Sahoo argued that the…”

Spinning strings and minimal surfaces in AdS 3 with mixed 3-form fluxes

“…Earlier studies of classical strings in AdS 3 with Neveu-Schwarz fluxes are [28][29][30]. In this paper we we solve the equations of motion of the classical folded spinning string solution in AdS 3 in terms of a perturbative expansion in the Neveu-Schwarz flux b.…”

Spiky strings onAdS3×S3with NS-NS flux

“…With these ideas, various large classes of rigidly rotating and pulsating string solutions have been studied in anti-de Sitter (AdS) and non-AdS backgrounds. These studies have also been successful in providing a realization of the string states which would correspond to some exact operators in the gauge theory side (see, for example [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]). In HM construction, the spectrum on the field theory side consists of an elementary excitation, the so-called magnon which carries a momentum p along the finitely or infinitely long spin chain [31,32].…”