We study giant magnons in the the D1-D5 system from both the boundary CFT and as classical solutions of the string sigma model in $AdS_3\times S^3\times T^4$. Re-examining earlier studies of the symmetric product conformal field theory we argue that giant magnons in the symmetric product are BPS states in a centrally extended $SU(1|1)\times SU(1|1)$ superalgebra with two more additional central charges. The magnons carry these additional central charges locally but globally they vanish. Using a spin chain description of these magnons and the extended superalgebra we show that these magnons obey a dispersion relation which is periodic in momentum. We then identify these states on the string theory side and show that here too they are BPS in the same centrally extended algebra and obey the same dispersion relation which is periodic in momentum. This dispersion relation arises as the BPS condition for the extended algebra and is similar to that of magnons in ${\cal N}=4$ Yang-Mills
We investigate the analytic structure of the magnon S-matrix in the spin-chain description of planar ${\cal N}=4$ SUSY Yang-Mills/$AdS_{5}\times S^{5}$ strings. Semiclassical analysis suggests that the exact S-matrix must have a large family of poles near the real axis in momentum space. In this article we show that these are double poles corresponding to the exchange of pairs of BPS magnons. Their locations in the complex plane are uniquely fixed by the known dispersion relation for the BPS particles. The locations precisely agree with the recent conjecture for the $S$ matrix by Beisert, Hern…
We compute the force and torque between well-separated, slowly-moving Giant Magnons with arbitrary orientations on S^5. We propose an effective Hamiltonian for Giant Magnons in this regime.
We produce the open strings on $\mathbb{R}\times S^{2}$ that correspond to the solutions of integrable boundary sine-Gordon theory by making use of the $N$-magnon solutions provided in \cite{KPV} together with explicit moduli. Relating the two boundary parameters in a special way we describe the scattering of giant magnons with non-maximal $Y=0$ giant gravitons and calculate the leading contribution to the associated magnon scattering phase.
We investigate dyonic giant magnons propagating on $γ$-deformed $AdS_5\times S^5$ by Neumann-Rosochatius reduction method with a twisted boundary condition. We compute finite-size effect of the dispersion relations of dyonic giant magnons which generalizes the previously known case of the giant magnons with one angular momentum found by Bykov and Frolov.
Magnon interactions give important contributions to the wrapping interactions of the N=4 spin-chain. Similar effects are expected for the finite size corrections to the giant magnon energy in AdS_5 x S^5. In this paper I review the finite gap description of giant magnons and the leading order calculation of the finite size corrections to the giant magnon dispersion relation for multi-magnon states.
In the string theory in AdS_4 \times CP^3 we construct the giant magnon and spike solutions with two spins in two kinds of subspaces of R_t \times CP^3 and derive the dispersion relations for them. For the single giant magnon solution in one subspace we show that its dispersion relation is associated with that of the big one-spin giant magnon solution in the RP^2 subspace. For the single giant magnon solution in the other complementary subspace its dispersion relation is similar to that of the one-spin giant magnon solution living in the S^2 subspace but has one additional spin dependence.
We consider D3-brane action in the maximally supersymmetric type IIB plane-wave background. Upon fixing the light-cone gauge, we obtain the light-cone Hamiltonian which is manifestly supersymmetric. The 1/2 BPS solutions of this theory (solutions which preserve 16 supercharges) are either of the form of spherical three branes, the giant gravitons, or zero size point like branes. We then construct specific classes of 1/4 BPS solutions of this theory in which static electric field on the brane is turned on. These solutions are deformations about either of the two 1/2 BPS solutions. In particular…
We study the conjectured exact S-matrix for the scattering of BPS magnon boundstates in the spin-chain description of planar N=4 SUSY Yang-Mills. The conjectured S-matrix exhibits both simple and double poles at complex momenta. Some of these poles lie parametrically close to the real axis in momentum space on the branch where particle energies are positive. We show that all such poles are precisely accounted for by physical processes involving one or more on-shell intermediate particles belonging to the known BPS spectrum.
We construct the full set of boundary giant magnons on $\mathbb{R}\times S^{2}$ attached to the maximal $Z=0$ giant graviton by mapping from the general solution to static sine-Gordon theory on the interval and compute the values of $Δ-J$ at finite $J$, including the leading order corrections when $J$ is large. We then consider the Born-Infeld theory of the giant graviton itself to construct BIon spike solutions that correspond to the world volume description of the boundary giant magnons at finite $J$.
We study the giant magnon solutions in the near horizon geometry of the Neveu-Schwarz (NS) 5-brane background. In conformal gauge, we find magnon dispersion relation in the large angular momentum (J) limit. We further show that the giant magnon poses uniform distribution of the angular momentum along the string world-sheet as in case of AdS_5\times S^5 spacetime.
We find the exact solution for a finite size Giant Magnon in the $SU(2)\times SU(2)$ sector of the string dual of the $\mathcal{N}=6$ superconformal Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. The finite size Giant Magnon solution consists of two magnons, one in each $SU(2)$. In the infinite size limit this solution corresponds to the Giant Magnon solution of arXiv:0806.4959. The magnon dispersion relation exhibits finite-size exponential corrections with respect to the infinite size limit solution.
Using finite gap methods, we find the leading order finite size corrections for an arbitrary number of giant magnons on physical strings, where the sum of the momenta is a multiple of 2π. Our results are valid for the Hofman-Maldacena fundamental giant magnons as well as their dyonic generalizations. The energy corrections turn out to be surprisingly simple, especially if all the magnons are fundamental, and at leading order are independent of the magnon flavors. We also show how to use the Bethe ansatz to find finite size corrections for dyonic giant magnons with large R-charges.
The quantization of the giant magnon away from the infinite size limit is discussed. We argue that this quantization inevitably leads to string theory on a Z_M-orbifold of S^5. This is shown explicitly and examined in detail in the near plane-wave limit.
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.
This paper studies giant magnons in AdS_4 x CP^3 using both the string sigma-model and the algebraic curve. We complete the dictionary of solutions by finding the dyonic generalisation of the CP^1 string solution, which matches the `small' giant magnon in the algebraic curve, and by pointing out that the solution recently constructed by the dressing method is the `big' giant magnon. We then use the curve to compute finite-J corrections to all cases, which for the non-dyonic cases always match the AFZ result. For the dyonic RP^3 magnon we recover the S^5 answer, but for the `small' and `big' gi…
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 obtain the giant magnon of Hofman-Maldacena and its dyonic generalisation on R x S^3 < AdS_5 x S^5 from the general elliptic finite-gap solution by degenerating its elliptic spectral curve into a singular curve. This alternate description of giant magnons as finite-gap solutions associated to singular curves is related through a symplectic transformation to their already established description in terms of condensate cuts developed in hep-th/0606145.
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 apply the dressing method to construct new classical string solutions describing various scattering and bound states of magnons. These solutions carry one, two or three SO(6) charges and correspond to multi-soliton configurations in the generalized sine-Gordon models.
We use the algebraic curve and Luscher's mu-term to calculate the leading order finite size corrections to the dispersion relation of giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3. We consider a single magnon as well as one magnon in each SU(2). In addition the algebraic curve computation is generalized to give the leading order correction for an arbitrary multi-magnon state in the SU(2) x SU(2) sector.
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.
From the Polyakov string action using a conformal gauge we construct a three-spin giant magnon solution describing a long open string in AdS_5 \times S^5 which rotates both in two angular directions of S^5 and in one angular direction of AdS_5. Through the Virasoro constraints the string motion in AdS_5 takes an effect from the string configuration in S^5. The dispersion relation of the soliton solution is obtained as a superposition of two bound states of magnons. We show that there is a correspondence between a special giant magnon in AdS_2 and the sinh-Gordon soliton.
We extend our earlier work by demonstrating how to construct classical string solutions describing arbitrary superpositions of scattering and bound states of dyonic giant magnons on S^5 using the dressing method for the SU(4)/Sp(2) coset model. We present a particular scattering solution which generalizes solutions found in hep-th/0607009 and hep-th/0607044 to the case of arbitrary magnon momenta. We compute the classical time delay for the scattering of two dyonic magnons carrying angular momenta with arbitrary relative orientation on the S^5.
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 find new 1/8-BPS giant graviton solutions in $AdS_5 \times S^5$, carrying three angular momenta along $S^5$, and investigate their properties. Especially, we show that nonzero worldvolume gauge fields are admitted preserving supersymmetry. These gauge field modes can be viewed as electromagnetic waves along the compact D3 brane, whose Poynting vector contributes to the BPS angular momenta. We also analyze the (nearly-)spherical giant gravitons with worldvolume gauge fields in detail. Expressing the $S^3$ in Hopf fibration ($S^1$ fibred over $S^2$), the wave propagates along the $S^1$ fiber.
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…
We investigate giant magnons from classical rotating strings in two different backgrounds. First we generalize the solution of Hofman and Maldacena and investigate new magnon excitations of a spin chain which are dual to a string on $R\times S^5$ with two non-vanishing angular momenta. Alowing string dynamics along the third angle in the five sphere, we find a dispersion relation that reproduces the Hofman and Maldacena and the one found by Dorey for the two spin case. In the second part of the paper we generalize the two "spin" giant magnon to the case of $\b$-deformed $\axs$ background. We f…
We study the fermion zero-mode dynamics for open strings ending on the giant graviton branes. For the open string ending on the Z=0 brane, the quantization of the fermion zero-modes of boundary giant magnons reproduces the 256 states of the boundary degrees with the precise realization of the SU(2|2) X SU(2|2) symmetry algebra. Also for the open string ending on the Y=0 brane, we reproduce the unique vacuum state from the fermion zero-modes.
A new example of AdS/CFT duality relating IIA string theory on AdS_4 x CP^3 to N=6 superconformal Chern-Simons theory has recently been provided by ABJM. By now a number of papers have considered particular giant magnon classical string solutions in the CP^3 background, corresponding to excitations in the spin chain picture of the dual field theory. In this paper we apply the CP^3 = SU(4)/S(U(3) x U(1)) dressing method to the problem of constructing general classical string solutions describing various configurations of giant magnons. As a particular application we present a new giant magnon s…
This paper studies giant magnons in CP3, which in all known cases are old solutions from S5 placed into two- and three-dimensional subspaces of CP3, namely CP1, RP2 and RP3. We clarify some points about these subspaces, and other potentially interesting three- and four-dimensional subspaces. After confirming that E-(J1-J4)/2 is a Hamiltonian for small fluctuations of the relevant 'vacuum' point particle solution, we use it to calculate the dispersion relation of each of the inequivalent giant magnons. We comment on the embedding of finite-J solutions, and use these to compare string solutions …
We perform a first-principles semi-classical computation of the one-loop corrections to the dispersion relation and S-matrix of Giant Magnons in AdS_5 x S^5 string theory. The results agree exactly with expectations based on the strong coupling expansion of the exact Asymptotic Bethe Ansatz equations. In particular we reproduce the Hernandez-Lopez term in the dressing phase.
We construct the general 1/2 BPS M2 giant graviton solutions asymptotic to the eleven-dimensional maximally supersymmetric plane wave background, based on the recent work of Lin, Lunin and Maldacena. The solutions have null singularity and we argue that it is unavoidable to have null singularity in the proposed framework, although the solutions are still physically relevant. They involve an arbitrary function F(x) which is shown to have a correspondence to the 1/2 BPS states of the BMN matrix model. A detailed map between the 1/2 BPS states of both sides is worked out.
In this paper we find giant magnon and single spike string solutions in a sector of the gamma-deformed conifold. We examine the dispersion relations and find a behavior analogous to the undeformed case. The transcendental functional relations between the conserved charges are shifted by certain gamma-dependent term. The latter is proportional to the total momentum and thus qualitatively different from known cases.
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.
Solitons in field theory provide a window into regimes not directly accessible by the fundamental perturbative degrees of freedom. Motivated by interest in the worldsheet S-matrix of string theory in AdS_5 x S^5 in the limit of infinite worldsheet volume we consider the semiclassical quantization of a particular soliton of this theory: the Hofman-Maldacena `giant magnon' spinning string. We obtain explicit formulas for the complete spectrum of bosonic and fermionic fluctuations around the giant magnon. As an application of these results we confirm that the one-loop correction to the classical …
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.
In this paper we study the solitonic string solutions of magnon and single spike type in the beta-deformed AdS_4 x CP3 background. We find the dispersion relations which are supposed to give the anomalous dimension of the gauge theory operators.
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…
We explicitly construct the eight fermion zero mode solutions for the Hofman-Maldacena giant magnon. The solutions are naturally gauge fixed under the κ-symmetry. Substituting the solutions back into the Lagrangian leads to a simple expression that can be quantized directly. We also show how to construct the SU(2|2)\times SU(2|2) superalgebra from these zero modes. For completeness we also find the four bosonic zero mode solutions.
We find explicit solutions for giant magnons and spiky strings on the squashed three dimensional sphere. For a special value of the squashing parameter the solutions describe strings moving in a sector of the conifold, while for another value of the squashing parameter we recover the known results on the round three dimensional sphere. A new feature is that the energy and the momenta enter in the dispersion relation of the conifold in a transcendental way.
We count 1/8-BPS states in type IIB string theory on AdS_5 x S^5 background which carry three independent angular momenta on S^5. These states can be counted by considering configurations of multiple dual-giant gravitons up to N in number which share at least four supersymmetries. We map this counting problem to that of counting the energy eigen states of a system of N bosons in a 3-dimensional harmonic oscillator. We also count 1/8-BPS states with two independent non-zero spins in AdS_5 and one non-zero angular momentum on S^5 by considering configurations of arbitrary number of giant gravito…
We study classical scattering phase of CP^2 dyonic giant magnons in R_t x CP^3. We construct two-soliton solutions explicitly by the dressing method. Using these solutions, we compute the classical time delays for the scattering of giant magnons, and compare them to boundstate S-matrix elements derived from the conjectured AdS_4/CFT_3 S-matrix by Ahn and Nepomechie in the strong coupling limit. Our result is consistent with the conjectured S-matrix. The dyonic solutions play an essential role in revealing the polarization dependence of scattering phase.
We show that the BPS spectrum of pure SU(3) four-dimensional super Yang-Mills with N=2 supersymmetry exhibits a surprising phenomenon: there are regions of the Coulomb branch where the growth of the BPS degeneracies with the charge is exponential. We show this using spectral networks and independently using wall-crossing formulae and quiver methods. The computations using spectral networks provide a very nontrivial example of how these networks determine the four-dimensional BPS spectrum. We comment on some physical implications of the wild spectrum: for example, exponentially many field-theor…
We consider giant magnons propagating in a γ-deformed AdS_5 x S^5 background obtained from AdS_5 x S^5 by means of a chain of TsT transformations. We point out that in the light-cone gauge and in the infinite J limit the deformed and undeformed string models share the same magnon dispersion relation, the \su(2|2)\oplus \su(2|2)-invariant world-sheet S-matrix and the dressing factor. The γ-dependence in the limit is only due to different level-matching conditions. We consider the reduction of the deformed model to R x S^3 and determine the leading γ-dependence of the dispersion relation for a f…
We consider classical string spectrum of R x CP^3, and construct a family of solutions with residual SU(2) symmetry by the dressing method on SU(4)/U(3) sigma model. All of them obey the square-root type dispersion relation, as is expected from the su(2|2) symmetry. A single dyonic giant magnon is not found in this approach.
The giant magnon is a rotating spiky string configuration which has the same dispersion relation between the energy and angular momentum as that of a spin magnon. In this paper we investigate the effects of the NS-NS and Melvin fields on the giant magnon. We first analyze the energy and angular momenta of the two-spin spiky D-string moving on the $AdS_3\times S^1$ with the NS-NS field. Due to the infinite boundary of the AdS spacetime the D-string solution will extend to infinity and it appears the divergences. After adding the counter terms we obtain the dispersion relation of the correspondi…
We study solutions for a rotating string on S^3 with a background NS-NS B-field and show the existence of spiky string and giant magnon as two limiting solutions. We make a connection to the sine-Gordon model via the Polyakov worldsheet action and study the effect of B-field. In particular, we find the magnon solution can be mapped to the excitation of a fractional spin chain. We conjecture a B-deformed SYM to be the gauge theory dual to this background.
We investigate giant and dual giant type BPS configurations in the near-horizon geometry of a certain 1/16-BPS AdS_5 black hole. By quantising the space of solutions we count the dual giant configurations and compare with the black hole entropy. This suggests a missing degeneracy factor which we argue comes from an angular momentum quantum number. From the D-brane world volume this arises from BPS electromagnetic waves. We study these waves in the context of giants and dual giants in the black hole near-horizon geometry. We further demonstrate that turning on waves on the world-volume of 1/8-B…
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 study the classical spectrum of string theory on AdS_5 X S^5 in the Hofman-Maldacena limit. We find a family of classical solutions corresponding to Giant Magnons with two independent angular momenta on S^5. These solutions are related via Pohlmeyer's reduction procedure to the charged solitons of the Complex sine-Gordon equation. The corresponding string states are dual to BPS boundstates of many magnons in the spin-chain description of planar N=4 SUSY Yang-Mills. The exact dispersion relation for these states is obtained from a purely classical calculation in string theory.
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 consider a D-brane type state which shares the characteristic of the recently found giant magnon of Hofman and Maldacena. More specifically we find a bound state of giant graviton (D3-brane) and giant magnon (F-string), which has exactly the same anomalous dimension as that of the giant magnon. It is described by the D3-brane with electric flux which is topologically a $S^3$ elongated by the electric flux. The angular momentum and energy are infinite, but split sensibly into two parts -- the infinite part precisely the same as that of the giant magnon and the finite part which can be identi…
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.
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.
