利用最近提出的N=6超Chern-Simons理论的S-矩阵导出的Luscher μ项公式，研究了AdS_4 x CP ^3上IIA型弦论的双子巨磁振子的有限尺寸效应.我们计算了对称组态的影响，其中两个外束缚态，每个A和B粒子，具有相同的动量p和自旋J_2。我们比较这与经典的弦论的结果，我们计算通过减少它的Neumann-Rosochatius系统。两个结果完全吻合。
英文摘要：
We consider finite-size effects for the dyonic giant magnon of the type IIA string theory on AdS_4 x CP^3 by applying Luscher mu-term formula which is derived from a recently proposed S-matrix for the N=6 super Chern-Simons theory. We compute explicitly the effect for the case of a symmetric configuration where the two external bound states, each of A and B particles, have the same momentum p and spin J_2. We compare this with the classical string theory result which we computed by reducing it to the Neumann-Rosochatius system. The two results match perfectly.
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.
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…
We show that the dressing transformation method produces a new type of dyonic CP^n magnon in terms of which all the other known solutions are either composites or arise as special limits. In particular, this includes the embedding of Dorey's dyonic magnon via an RP^3 subspace of CP^n. We also show how to generate Dorey's dyonic magnon directly in the S^n sigma model via the dressing method without resorting to the isomorphism with the SU(2) principle chiral model when n=3. The new dyon is shown to be either a charged dyon or topological kink of the related symmetric-space sine-Gordon theories …
We compute quantum corrections to finite-size effects for various dyonic giant magnons in the AdS_4 x CP^3 in two different approaches. The off-shell algebraic curve method is used to quantize the classical string configurations in semi-classical way and to compute the corrections to the string energies. These results are compared with the F-term Lüscher formula based on the S-matrix of the AdS_4 / CFT_3. The fact that the two results match exactly provides another stringent test for the all-loop integrability conjecture and the exact S-matrix based on it.
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 investigate the two- and three-point correlation functions of the dyonic magnon and spike, which correspond to the solitonic string moving in the Poincare AdS and three-dimensional sphere. We show that the coupling between two dyonic magnons or spikes together with a marginal scalar operator in the string theory is exactly the same as one obtained by the RG analysis in the gauge theory.
We clarify the higher-dimensional origin of a class of dyonic gaugings of $D=4$ ${\cal N}=8$ supergravity recently discovered, when the gauge group is chosen to be ISO(7). This dyonically-gauged maximal supergravity arises from consistent truncation of massive IIA supergravity on $S^6$, and its magnetic coupling constant descends directly from the Romans mass. The critical points of the supergravity uplift to new AdS$_4$ massive type IIA vacua. We identify the corresponding CFT$_3$ duals as super-Chern-Simons-matter theories with simple gauge group SU$(N)$, with level $k$ given by the Romans m…
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.
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…
We present a semiclassical derivation of the tree-level and 1-loop dressing phases in the massive sector of string theory on AdS_3 x S^3 x T^4 supplemented by R-R and NS-NS 3-form fluxes. In analogy with the AdS_5 x S^5 case, we use the dressing method to obtain scattering solutions for dyonic giant magnons which allows us to determine the semiclassical bound-state S-matrix and its 1-loop correction. We also find that the 1-loop correction to the dyonic giant magnon energy vanishes. Looking at the relation between the bound-state picture and elementary magnons in terms of the fusion procedure …
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 study classical and quantum finite-size corrections to giant magnons in AdS_4 x CP^3 using generalised Lüscher formulae. Lüscher F-terms are organised in powers of the exponential suppression factor exp(-Delta/2h)^m, and we calculate all terms in this series, matching one-loop algebraic curve results from our previous paper arXiv:1006.2174. Starting with the second term, the structure of these terms is different to those in AdS_5 x S^5 thanks to the appearance of heavy modes in the loop, which can here be interpreted as two-particle bound states in the mirror theory. By contrast, physical b…
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.
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 first law of thermodynamics of dyonic black strings carrying a linear momentum in type IIA string theory compactified on K3 with leading order $α'$ corrections. The low energy effective action contains mixed Chern-Simons terms of the form $-2B_{(2)}\wedge {\rm tr}(R(Γ_\pm)\wedge R(Γ_\pm))$ which is equivalent to $2H_{(3)}\wedge \mathrm{CS}_{(3)}(Γ_\pm)$ up to a total derivative. We find that the naive application of Wald entropy formula leads to two different answers associated with the two formulations of the mixed Chern-Simons terms. Surprisingly, neither of them satisfies the f…
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.
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…
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 compute both classical and quantum finite-size corrections at leading order in the strong coupling limit for the (dyonic) giant magnon in the Lunin-Maldacena background. Based on the exact S-martix conjectured for the deformed theory, we generalize the Luscher formula to include twisted boundary conditions and show that the results match with those derived both by finite-size classical solutions of the giant magnon and by algebraic curve analysis.
Giant magnons are one of the main manifestations of integrability on the string theory side of the AdS/CFT correspondence. Motivated by the recent advances in their study, especially in the context of the string theory dual of ABJM theory, we present and prove explicit N-soliton solutions for the relevant CP^n, SU(n) and S^n sigma models. The proof is based on solving the dressing method recursion with the help of determinant operations, and our solutions hold for any choice of vacuum and soliton parameters. We further specialize our results for the choices that lead to giant magnons, and as a…
We consider a certain ${\cal N}=1$ supersymmetric, SO(3)$\times$SO(3) invariant, subsector of the dyonic ISO(7)-gauged maximal supergravity in four-dimensions. The theory contains two scalar fields and two pseudoscalar fields. We look for stationary points of the scalar potential, especially the one preserving ${\cal N}=3$ supersymmetry of the original ISO(7) gauged theory. The ${\cal N}=3$ stationary point corresponding to the $AdS$ vacuum in the $D=4$ theory is lifted to a warped $AdS_4\times X_6$ type solution in massive type IIA supergravity. This $D=10$ background should be the dual of a …
We construct black holes with a Ricci flat horizon in Einstein--Yang-Mills theory with a negative cosmological constant, which approach asymptotically an AdS$_d$ spacetime background (with $d\geq 4$). These solutions are isotropic, $i.e.$ all space directions in a hypersurface of constant radial and time coordinates are equivalent, and possess both electric and magnetic fields. We find that the basic properties of the non-Abelian solutions are similar to those of the dyonic isotropic branes in Einstein-Maxwell theory (which, however, exist in even spacetime dimensions only). These black branes…
We address the question about the exact form of the dispersion relation for light-cone string excitations in string theory in AdS3 x S3 x T4 with mixed R-R and NS-NS 3-form fluxes. The analogy with string theory in AdS5 x S5 suggests that in addition to the data provided by the perturbative near-BMN expansion and the symmetry algebra considerations there is also another source of information about the dispersion relation -- the semiclassical giant magnon solution. In earlier work in arXiv:1303.1037 and arXiv:1304.4099 it was found that the symmetry algebra constraints consistent with perturbat…
We investigate a strong coupling expansion of N=6 superconformal Chern-Simons theory obtained from the semiclassical analysis of low energy, effective degrees of freedom given by the eigenvalues of a certain matrix model. We show how the orbifolded sphere S^7/Z_k of the dual geometry emerges dynamically from the distribution of the eigenvalues. As a test of this approach we compute the energy of off-diagonal excitations, finding perfect agreement with the dispersion relation of giant magnons.
Using N=2 superspace techniques we compute the four-loop spectrum of single trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric Chern-Simons theories. Our computation yields a four-loop contribution to the function h^2(λ) (and its ABJ generalization) in the magnon dispersion relation which has fixed maximum transcendentality and coincides with the findings in components given in the revised versions of arXiv:0908.2463 and arXiv:0912.3460. We also discuss possible scenarios for an all-loop function h^2(λ) that interpolates between weak and strong couplings.
推广了贝伦斯坦、科雷亚和巴斯克斯的hep-th/0509015的思想，我们研究了在R × S ^[3]上由N=4的SU（N）超杨-米尔斯得到的约化矩阵量子力学的SU（2）扇区中的多磁振子态。一般的Q-磁振子态被描述为连接背景矩阵的Q+1本征值的"串比特“链，其在大N极限中形成1/2 BPS圆形液滴。我们将集中讨论第一个和最后一个本征值位于液滴边缘的无限长态。一般来说，每个组成的弦比特都有一个复准动量，而状态的总准动量P是实数。对于给定的Q和P，当Q+1个本征值等间距地分布在连接两个最外本征值的同一条线段上时，弦比特链的能量最小。这种束缚弦比特的配置精确地再现了经典弦论中双子巨磁振子的色散关系。我们还显示了出现的双自旋折叠/圆形字符串在特殊的无限自旋极限的特殊配置的封闭链的字符串位。
We consider operators in ${\cal N}=4$ super Yang-Mills theory dual to closed string states propagating on a class of LLM geometries. The LLM geometries we consider are specified by a boundary condition that is a set of black rings on the LLM plane. When projected to the LLM plane, the closed strings are polygons with all corners lying on the outer edge of a single ring. The large $N$ limit of correlators of these operators receives contributions from non-planar diagrams even for the leading large $N$ dynamics. Our interest in these fluctuations is because a previous weak coupling analysis argu…
In arXiv:0908.2463 we computed the four-loop correction to a function depending on the 't Hooft coupling(s) that appears in the magnon dispersion relation of the spin chains derived from single trace operators in N=6 superconformal Chern-Simons theories. In this paper we give detailed descriptions of this calculation and the computation of the four-loop wrapping corrections for a length four operator in the 20 of SU(4), the R-symmetry group for these theories. Here, we give all relevant Feynman diagrams and loop integrals explicitly, and also demonstrate the cancellation of double poles in the…
The existence of a nontrivial interpolating function h(λ) is one of the novel features of the new AdS4/CFT3 correspondence involving ABJM theory. At strong coupling, most of the investigation of semiclassical effects so far has been for strings in the AdS4 sector. Several cutoff prescriptions have been proposed, leading to different predictions for the constant term in the expansion h(λ)=\sqrt{λ/2} + c + ... . We calculate quantum corrections for giant magnons, using the algebraic curve, and show by comparing to the dispersion relation that the same prescriptions lead to the same values of c i…
Recently Martelli and Sparks presented the first non-toric AdS_4/CFT_3 duality relation between M-theory on AdS_4 x V_{5,2}/Z_k and a class of three-dimensional N=2 quiver Chern-Simons-matter theories. V_{5,2} is a seven-dimensional homogeneneous Sasaki-Einstein manifold with isometry group SO(5)xU(1)_R, which is in general broken to SU(2)xU(1)xU(1)_R by the orbifold projection if k>1. The dual field theory is described by the A_1 quiver, U(N)_k x U(N)_{-k} gauge group, four bifundamentals, two adjoint chiral multiplets interacting via a cubic superpotential. We explore this proposal by studyi…
本文研究了平面规范理论，其中某个规范群G自发破缺为一个有限子群H。该光谱由磁涡旋，全球H电荷和双子组合表现出拓扑Aharonov-Bohm相互作用。除其他事项外，我们审查的Hopf代数D（H）相关的剩余离散H规范理论，它提供了一个统一的描述上述粒子的自旋，编织和融合的性质。加入陈-西蒙斯（CS）长期到这些模型的影响也得到了解决。我们记得紧规范群G的CS作用量可以用上同调群H^4（BG，Z）来分类。对于有限群H，这种分类归结为上同调群H^3（H，U（1））。因此，有限群H的不同CS作用由H的不等价3-上圈给出。我们认为，在破缺规范群G中加入CS作用量会导致由剩余有限规范群H的3-上循环所支配的涡旋的额外拓扑相互作用，该剩余有限规范群H由从H^4（BG，Z）到H^3（H，U（1））的自然同态所确定。相应地，相关的Hopf代数D（H）被变形为拟Hopf代数。这些一般性的考虑可以用CS理论来说明，在CS理论中，某些U（1）规范群的直积被分解为一个有限子群H。结果表明，对于有限阿贝尔规范群H，并不是所有可能的3-上圈都可以用这种方法得到。那些没有达到的是最有趣的。例如，由这样一个3-上圈给出的Z_2 x Z_2 x Z_2 CS理论与具有非交换规范群（8阶二面体群）的普通规范理论是对偶的。最后，对非交换有限规范群为二面角群或双二面角群的CS理论也作了详细的讨论。
