Giant Magnon Solutions Research Articles

Open giant magnons suspended between dual giant gravitons in mathcal{N} = 4 SYM

We study classical solutions to the Nambu-Goto string on AdS2× S1 and AdS3× S1 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.

Double Yang-Baxter deformation of spinning strings

We study the reduction of classical strings rotating in the deformed three- sphere truncation of the double Yang-Baxter deformation of the AdS3×S3×T4 background to an integrable mechanical model. The use of the generalized spinning-string ansatz leads to an integrable deformation of the Neumann-Rosochatius system. Integrability of this system follows from the fact that the usual constraints for the Uhlenbeck constants apply to any deformation that respects the isometric coordinates of the three-sphere. We construct solutions to the system in terms of the underlying ellipsoidal coordinate. The solutions depend on the domain of the deformation parameters and the reality conditions of the roots of a fourth order polynomial. We obtain constant-radii, giant-magnon and trigonometric solutions when the roots degenerate, and analyze the possible solutions in the undeformed limit. In the case where the deformation parameters are purely imaginary and the polynomial involves two complex-conjugated roots, we find a new class of solutions. The new class is connected with twofold giant-magnon solutions in the degenerate limit of infinite period.

Giant magnons and spiky strings in the Schr\xf6dinger/dipole-deformed CFT correspondence

We construct semi-classical string solutions of the Schrödinger Sch5 ×S5 spacetime, which is conjectured to be the gravity dual of a non-local dipole-deformed CFT. They are the counterparts of the giant magnon and spiky string solutions of the undeformed AdS5 × S5 to which they flow when the deformation parameter is turned off. They live in an S3 subspace of the five-sphere along the directions of which the B-field has non-zero components, having also extent in the Sch5 part of the metric. Finally, we speculate on the form of the dual field theory operators.

Giant magnons of string theory in the lambda background

The analogues of giant magnon configurations are studied on the string world sheet in the lambda background. This is a discrete deformation of the AdS5×S5 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 shown in the semi-classical limit to be described by the quantum S-matrix that is a quantum group deformation of the conventional giant magnon S-matrix. It is further shown that in the small g limit, a sector of the S-matrix is related to the XXZ spin chain whose spectrum matches the spectrum of magnon bound states.

SL(2,\xa0Z) invariant rotating (m,\xa0n) strings in AdS_3times S^3 with mixed flux

We study rigidly rotating and pulsating (m, n) strings in AdS_3 times S^3 with mixed three form flux. The AdS_3 times S^3 background with mixed three form flux is obtained in the near horizon limit of SL(2, Z)-transformed solution, corresponding to the bound state of NS5-branes and fundamental strings. We study the probe (m, n)-string in this background by solving the manifest SL(2, Z)-covariant form of the action. We find the dyonic giant magnon and single spike solutions corresponding to the equations of motion of a probe string in this background and find various relationships among the conserved charges. We further study a class of pulsating (m, n) string in AdS_3 with mixed three form flux.

The exact spectrum and mirror duality of the (AdS5 × S 5) η superstring

We discuss the spectrum of a string propagating on η-deformed AdS5 × S5 by treating its worldsheet theory as an integrable quantum field theory. The exact S-matrix of this field theory is given by a qdeformation of the AdS5 × S5 worldsheet S-matrix with a real deformation parameter. By considering mirror (double Wick-rotated) versions of these worldsheet theories, we give the thermodynamic Bethe ansatz description of their exact finite-size spectra. Interestingly, this class of models maps onto itself under the mirror transformation. At the string level, this seems to indicate that the light-cone worldsheet theories of strings on particular pairs of backgrounds are related by a double Wick rotation, a feature we call “mirror duality.” We provide a partial verification of these statements at the level of a sigma model by considering reduced actions and their corresponding (mirror) giant magnon solutions.

String solutions inAdS3×S3×T4with NS-NSB-field

We develop an approach for solving the string equations of motion and Virasoro constraints in any background which has some (unfixed) number of commuting Killing vector fields. It is based on a specific ansatz for the string embedding. We apply the above mentioned approach for strings moving inAdS_3 x S^3 x T^4 with 2-form NS-NS B-field. We succeeded to find solutions for a large class of string configurations on this background. In particular, we derive dyonic giant magnon solutions in the R_t x S^3 subspace, and obtain the leading finite-size correction to the dispersion relation.

Giant magnon on deformedAdS3×S3

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.

Worldsheet one-loop energy correction to IIA giant magnon

We compute one-loop corrections to the energy of a IIA giant magnon solution in the AdS4×ℂP3 background by using the standard quantum field theory (QFT) techniques. The string action is expanded around the solution to the quadratic order in the fluctuation fields. The resulting action has 2D coordinate dependent-coefficients, a feature that complicates the analysis. The solution contains a worldsheet velocity parameter v, and is expanded in terms of the parameter. A perturbative analysis is carried out by treating the v-dependent parts as vertices. The energy is computed by first putting the system in a box of length L and Fourier-transforming the fields into discrete momentum modes. We compare our result with the results obtained by the algebraic curve method.

S-duality and the giant magnon dispersion relation

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 dependence compatible with S-duality.

Giant magnon solution and dispersion relation in string theory in [formula omitted] with mixed flux

We address the question of the exact form of the dispersion relation for light-cone string excitations in string theory in AdS3×S3×T4 with mixed R–R and NS–NS 3-form fluxes. The analogy with string theory in AdS5×S5 suggests that in addition to the data provided by the perturbative near-BMN expansion and symmetry algebra considerations there is another source of information for the dispersion relation – the semiclassical giant magnon solution. In earlier work in arXiv:1303.1037 and arXiv:1304.4099 we found that the symmetry algebra constraints, which are consistent with a perturbative expansion, do not completely determine the form of the dispersion relation. The aim of the present paper is to fix the dispersion relation by constructing a generalisation 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 (with coefficient q). We find that the angular momentum of this soliton gets shifted by a term linear in world-sheet momentum p. 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.

Finite-size corrections of the ℂℙ3giant magnons: the Lüscher terms

We compute classical and first quantum finite-size corrections to the recently found giant magnon solutions in two different subspaces of 3. We use the Lüscher approach on the recently proposed exact S-matrix for = 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 AdS4/CFT3 correspondence within an integrability framework.

Dressed giant magnons on ℂℙ3

A new example of AdS/CFT duality relating IIA string theory on AdS4 × 3 to = 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 3 background, corresponding to excitations in the spin chain picture of the dual field theory. In this paper we apply the 3 = SU(4)/S(U(3) × 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 solution on 3. Interestingly the dressed solution carries only a single SO(6) charge, in contrast with the dyonic magnons found in previous applications of the dressing method.

Finite size giant magnons in the string dual of 𝒩 = 6 superconformal Chern-Simons theory

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.

Giant magnon and spike solutions with two spins inAdS4×CP3

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.

The [formula omitted] sector in the string dual of [formula omitted] superconformal Chern–Simons theory

We examine the string dual of the recently constructed N = 6 superconformal Chern–Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). We focus in particular on the SU ( 2 ) × SU ( 2 ) sector. We find a sigma-model limit in which the resulting sigma-model is two Landau–Lifshitz models added together. We consider a Penrose limit for which we can approach the SU ( 2 ) × SU ( 2 ) sector. Finally, we find a new Giant Magnon solution in the SU ( 2 ) × SU ( 2 ) sector corresponding to one magnon in each SU ( 2 ) . We put these results together to find the full magnon dispersion relation and we compare this to recently found results for ABJM theory at weak coupling.

Exact solutions forN-magnon scattering

Giant magnon solutions play an important role in various aspects of the AdS/CFT correspondence. We apply the dressing method to construct an explicit formula for scattering states of an arbitrary number N of magnons on × S3. The solution can be written in Hirota form and in terms of determinants of N × N matrices. Such a representation may prove useful for the construction of an effective particle Hamiltonian describing magnon dynamics.

Quantum wrapped giant magnon

Understanding the finite-size corrections to the fundamental excitations of a theory is the first step towards completely solving for the spectrum in finite volume. We compute the leading exponential correction to the quantum energy of the fundamental excitation of the light-cone gauged string in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$, which is the giant magnon solution. We present two independent ways to obtain this correction: the first approach makes use of the algebraic curve description of the giant magnon. The second relies on the purely field-theoretical L\"uscher formulas, which depend on the world-sheet$S$-matrix. We demonstrate the agreement to all orders in $(\ensuremath{\Delta}/\sqrt{\ensuremath{\lambda}}{)}^{\ensuremath{-}1}$ of these approaches, which, in particular, presents a further test of the $S$-matrix. We comment on generalizations of this method of computation to other string configurations.

Gauge invariant finite size spectrum of the giant magnon

It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform light-cone gauge parameter. The resulting finite size effects are exponentially small in the R-charge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model.

Giant magnon in NS5-brane background

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.