A dynamic su(1|1)^2 S-matrix for AdS3/CFT2

We derive the S-matrix for the d(2,1;alpha)^2 symmetric spin-chain of AdS3/CFT2 by considering the centrally extended su(1|1)^2 algebra acting on the spin-chain excitations. The S-matrix is determined uniquely up to four scalar factors, which are further constrained by a set of crossing relations. The resulting scattering includes non-trivial processes between magnons of different masses that were previously overlooked.Comment: 41 pages, 4 figures. v2: corrected a misprint in appendix E, updated references, corrected some typos. v3: added a new appendix F with comparison to the literature, changed notation for the crossing equations, added references. Published versio

All-loop Bethe ansatz equations for AdS3/CFT2

Using the S-matrix for the d(2,1;alpha)^2 symmetric spin-chain of AdS3/CFT2, we propose a new set of all-loop Bethe equations for the system. These equations differ from the ones previously found in the literature by the choice of relative grading between the two copies of the d(2,1;alpha) superalgebra, and involve four undetermined scalar factors that play the role of dressing phases. Imposing crossing symmetry and comparing with the near-BMN form of the S-matrix found in the literature, we find several novel features. In particular, the scalar factors must differ from the Beisert-Eden-Staudacher phase, and should couple nodes of different masses to each other. In the semiclassical limit the phases are given by a suitable generalization of Arutyunov-Frolov-Staudacher phase.Comment: 26 pages, 2 figures. v2: references added. v3: changed notation for the crossing equations, added references. Published versio

Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J

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' giant magnons we obtain new corrections.Comment: 22 pages, 3 figures, 2 tables. v2 adds note on breather solution, and minor clarification

Worldsheet kinematics, dressing factors and odd crossing in mixed-flux AdS3 backgrounds

String theory on AdS_3 x S^3 x T^4 geometries supported by a combination of NS-NS and R-R charges is believed to be integrable. We elucidate the kinematics and analytic structure of worldsheet excitations in mixed charge and pure NS-NS backgrounds, when expressed in momentum, Zhukovsky variables and the rapidity $u$ which appears in the quantum spectral curve. We discuss the relations between fundamental and bound state excitations and the role of fusion in constraining and determining the S matrices of these theories. We propose a scalar dressing factor consistent with a novel $u$-plane periodicity and comment on its close relation to the XXZ model at roots of unity. We solve the odd part of crossing and show that our solution is consistent with fusion and reduces in the relativistic limit to dressing phases previously found in the literature.Comment: 53 pages, 77 figures. v2: added missing reference, fixed typo

Non-relativistic string monodromies

Spectral curve methods proved to be powerful techniques in the context of relativistic integrable string theories, since they allow to derive the semiclassical spectrum from the minimal knowledge of a Lax pair and a classical string solution. In this paper we initiate the study of the spectral curve for non-relativistic strings in AdS$_5\times S^5$. First we show that for string solutions whose Lax connection is independent of $\sigma$, the eigenvalues of the monodromy matrix do not have any spectral parameter dependence. We remark that this particular behaviour also appears for relativistic strings in flat space. Second, for some simple non-relativistic string solutions where the path ordered exponential of the Lax connection can be computed, we show that the monodromy matrix is either diagonalisable with quasi-momenta independent of the spectral parameter, or non-diagonalisable. For the latter case, we propose a notion of generalised quasi-momenta, based on maximal abelian subalgebras, which retain a dependence on the spectral parameter.Comment: 20 page

The effectiveness of relativistic invariance in AdS(3)

We use relativistic invariance to investigate two aspects of integrable AdS3 string theory. Firstly, we write down the all-loop TBA equations for the massless sector of the theory with R-R flux, using the recently discovered hidden relativistic symmetry. Secondly, for the low-energy relativistic limit of the theory with NS-NS flux we write down the S matrix, dressing factors and TBA. We find that the integrable system coincides with a restriction to AdS3 of the relativistic q-deformed AdS5 theory. We also comment on the relativistic limit of the small-k NS-NS theory

Towards the All-Loop Worldsheet S Matrix for AdS3 × S3 × T4

We obtain the all-loop worldsheet S matrix for fundamental excitations on AdS3 × S3 × T4 by studying the off-shell symmetry algebra of the superspace action in light cone gauge. The massless modes, unaccounted for in earlier works, are automatically included in our treatment. Their exact dispersion relation is found to be nonrelativistic, of giant-magnon form, and their scattering is naturally well defined. This opens the way to a complete investigation of AdS3/CFT2 integrability