We compute classical and first quantum finite-size corrections to the recently found giant magnon solutions in two different subspaces of $\mathbb{CP}^3$. We use the Lüscher approach on the recently proposed exact S-matrix for $\mathcal{N}=6$ superconformal Chern-Simons theory. We compare our results with the string and algebraic curve computations and find agreement, thus providing a non-trivial test for the new $AdS_4/CFT_3$ correspondence within an integrability framework.
This is a talk delivered at the Workshop on Quantum Fields and Strings of the 2014 Corfu Summer Institute. We discuss how giant magnons emerge in the context of the AdS5/CFT4 correspondence as the gravity duals of N = 4 super Yang-Mills magnon excitations. Then we present a new analytic expression for the dispersion relation of classical finite-size giant magnons with Lambert's W-function.
Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J
本文用弦σ模型和代数曲线研究了AdS_4 x CP^3中的巨磁振子。我们通过找到CP ^1弦解的双音推广（它与代数曲线中的“小”巨磁振子相匹配），并指出最近用dressing方法构造的解是“大”巨磁振子，来完成解的字典。然后，我们使用的曲线来计算有限J修正的所有情况下，这对于非双音的情况下总是匹配AFZ的结果。对于双介子RP^3磁振子，我们恢复了S^5的答案，但是对于“小”和“大”的巨磁振子，我们得到了新的修正。
The giant magnons are classical solitons of the O(N) sigma-model, which play an important role in the AdS/CFT correspondence. We study quantum giant magnons first at large N and then exactly using Bethe Ansatz, where giant magnons can be interpreted as holes in the Fermi sea. We also identify a solvable limit of Bethe Ansatz in which it describes a weakly-interacting Bose gas at zero temperature. The examples include the O(N) model at large N, weakly interacting non-linear Schrodinger model, and nearly isotropic XXZ spin chain in the magnetic field.
The analogues of giant magnon configurations are studied on the string world sheet in the lambda background. This is a discrete deformation of the AdS(5)xS(5) background that preserves the integrability of the world sheet theory. Giant magnon solutions are generated using the dressing method and their dispersion relation is found. This reduces to the usual dyonic giant magnon dispersion relation in the appropriate limit and becomes relativistic in another limit where the lambda model becomes the generalized sine-Gordon theory of the Pohlmeyer reduction. The scattering of giant magnons is then …
We consider strings moving in the R_t x S^3_ηsubspace of the η-deformed AdS_5 x S^5 and obtain a class of solutions depending on several parameters. They are characterized by the string energy and two angular momenta. Finite-size dyonic giant magnon belongs to this class of solutions. Further on, we restrict ourselves to the case of giant magnon with one nonzero angular momentum, and obtain the leading finite-size correction to the dispersion relation.
We investigate finite-size giant magnons propagating on γ-deformed AdS_4 x CP^3_γ type IIA string theory background, dual to one parameter deformation of the N=6 super Chern-Simoms-matter theory. Analyzing the finite-size effect on the dispersion relation, we find that it is modified compared to the undeformed case, acquiring γdependence.
We studied the finite-size giant magnons in $\text{AdS}_4\times\text{CP}^3_β$ background using the classical spectral curve constructed in this paper. We computed the finite-size corrections to the dispersion relations for the $RP^3$ giant magnons using our twisted algebraic curve based on the method proposed in arXiv:0810.1246, in which the authors computed the finite-size corrections of giant magnons in $\text{AdS}_4\times\text{CP}^3$ by introducing a finite-size resolvent $G_{\text{finite}}(x)$. We obtained exactly the same result as in arXiv:1106.3686, where a totally different approach wa…
We use S-duality and planarity to propose an argument for the non-renormalization of the dispersion relation of giant magnon solutions in type IIB string theory on AdS_5 x S^5. We compute the spectrum of giant magnons for (p,q)-strings from field theory at strong coupling by using the central charge properties of electrically and magnetically charged supersymmetric states in the Coulomb branch of N=4 super Yang-Mills. We argue that the coupling dependence of the giant magnon dispersion relation conjectured in the literature using integrability assumptions is in fact the only functional depende…
We study classical solutions to the Nambu-Goto string on $AdS_2 \times S^1$ and $AdS_3 \times S^1$ corresponding to strings stretched between wrapped branes extending in $AdS$. The solutions are obtained by analytic continuation of giant magnon solutions, cut at the position of the branes. These solutions carry one or two $SO(2,4)$ charges and a single $SO(6)$ charge. We compute their energies and show their relation to $\frac{1}{2}$-BPS geometries. Their relevance to the $SL(2)$ sector of $\mathcal{N}=4$ SYM is also discussed.
We obtain explicit formulas for the eight bosonic and eight fermionic fluctuations around the mixed-flux generalization of the Hofman-Maldacena giant magnon on AdS$_3 \times$S$^3 \times$T$^4$ and AdS$_3 \times$S$^3 \times$S$^3 \times$S$^1$. As a check of our results, we confirm that the semiclassical quantization of these fluctuations leads to a vanishing one-loop correction to the magnon energy, as expected from symmetry based arguments.
In this paper we consider the finite size effects for the strings in β-deformed AdS_{5}\times T^{1,1} background. We analyze the finite size corrections for the cases of giant magnon and single spike string solution. The finite size corrections for the undeformed case are straightforwardly obtained sending the deformation parameter to zero.
We generalize the method of our recent paper on the large-spin expansions of Gubser-Klebanov-Polyakov (GKP) strings to the large-spin and large-winding expansions of finite-size giant magnons and finite-size single spikes. By expressing the energies of long open strings in RxS2 in terms of Lambert's W-function, we compute the leading, subleading and next-to-subleading series of classical exponential corrections to the dispersion relations of Hofman-Maldacena giant magnons and infinite-winding single spikes. We also compute the corresponding expansions in the doubled regions of giant magnons an…
In this paper we have found a classical giant magnon-like solution with both infinite and finite angular momentum moving in Sch_5 x S^5 with B-field, which is believed to be dual to dipole-deformed N=4 super Yang-Mills theory. This string state propagates as a point particle in non-trivial subspace of the Sch_5 space but shows a giant magnon-like property in the S^2 subspace. We derive the energy-momentum dispersion relations and their finite-size correction for the case of finite but large angular momentum.
We study giant magnon solutions for strings moving on a deformed AdS(3)xS(3) background. We impose a conformal gauge on the Polyakov action and proceed with solving the Virasoro constraints. The expressions of the conserved charge J and the energy of a single magnon excitation are then computed. Then we determine the dispersion relation in the infinite J limit configuration and we find that it reduces to celebrated Hofman-Maldacena dispersion relation when the deformation parameter goes to zero.
We show nonrelativistic (NR) giant magnon dispersion relations by probing the torsional Newton Cartan (TNC) geometry with (semi)classical nonrelativistic rigidly rotating strings. We construct NR sigma models over $ R \times S^2 $ and consider two specific limiting cases those are of particular interest. Both of these limiting conditions give rise to what we identify as the \emph{small} momentum limit of the giant magnon dispersion relation in the dual SMT at \emph{strong} coupling. We further generalize our results in the presence of background NS-NS fluxes. Our analysis reveals that unlike i…
Three-point correlation functions in the strong-coupling regime of the AdS/CFT correspondence can be analyzed within a semiclassical approximation when two of the vertex operators correspond to heavy string states having large quantum numbers while the third vertex corresponds to a light state with fixed charges. We consider the case where the heavy string states are chosen to be giant magnon solitons with either a single or two different angular momenta, for various different choices of light string states.
We compute semiclassical three-point correlation function, or structure constant, of two finite-size (dyonic) giant magnon string states and a light dilaton mode in the Lunin-Maldacena background, which is the γ-deformed, or TsT-transformed AdS_5 x S_γ^5, dual to N = 1 super Yang-Mills theory. We also prove that an important relation between the structure constant and the conformal dimension, checked for the N = 4 super Yang-Mills case, still holds for the γ-deformed string background.
We compute holographic three-point correlation functions or structure constants of a zero-momentum dilaton operator and two (dyonic) giant magnon string states with a finite-size length in the semiclassical approximation. We show that the semiclassical structure constants match exactly with the three-point functions between two su(2) magnon single trace operators with finite size and the Lagrangian in the large 't Hooft coupling constant limit. A special limit J>>sqrt(lambda) of our result is compared with the relevant result based on the Lüscher corrections.
We explicitly construct the four and two fermion zero modes for the mixed-flux generalization of the Hofman-Maldacena giant magnon on two of the AdS$_3$ backgrounds with maximal amount of supersymmetry, AdS$_3 \times$S$^3 \times$T$^4$ and AdS$_3 \times$S$^3 \times$S$^3 \times$S$^1$. We also show how to get the $\mathfrak{psu}(1|1)^4$ and $\mathfrak{su}(1|1)^2$ superalgebras from the semiclassically quantized fermion zero modes.
In this note, we summarize recent progress in constructing and then semi-classically quantizing solitons, or non-abelian Q-balls, in the symmetric space sine-Gordon theories. We then consider the images of these solitons in the related constrained sigma model, which are the dyonic giant magnons on the string theory world-sheet. Focussing on the case of the symmetric space S^5, we perform a semi-classical quantization of the solitons and magnons and show that both lead to Chern-Simons quantum mechanics on the internal moduli space which is a real Grassmannian SO(4)/SO(2)xSO(2) but---importantly…
