We bootstrap the all-loop dynamic S-matrix for the homogeneous psu(1, 1|2) 2 spinchain believed to correspond to the discretization of the massive modes of string theory on AdS 3 × S 3 × T 4 . The S-matrix is the tensor product of two copies of the su(1|1) 2 invariant S-matrix constructed recently for the d(2, 1; α) 2 chain, and depends on two antisymmetric dressing phases. We write down the crossing equations that these phases have to satisfy. Furthermore, we present the corresponding Bethe Ansatz, which differs from the one previously conjectured, and discuss how our construction matches several recent perturbative calculations.

We derive the S-matrix for the d(2, 1; α) 2 symmetric spin-chain of AdS 3 /CFT 2 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.

Abstract:We derive the non-perturbative worldsheet S matrix for fundamental excitations of Type IIB superstring theory on AdS 3 × S 3 × T 4 with Ramond-Ramond flux. To this end, we study the off-shell symmetry algebra of the theory and its representations. We use these to determine the S matrix up to scalar factors and we derive the crossing equations that these scalar factors satisfy. Our treatment automatically includes fundamental massless excitations, removing a long-standing obstacle in using integrability to study the AdS 3 /CFT 2 correspondence. The present paper contains a detailed derivation of results first announced in arXiv:1403.4543.

This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractWe determine the all-loop dressing phases of the AdS 3 /CFT 2 integrable system related to type IIB string theory on AdS 3 ×S 3 ×T 4 by solving the recently found crossing relations and studying their singularity structure. The two resulting phases present a novel structure with respect to the ones appearing in AdS 5 /CFT 4 and AdS 4 /CFT 3 . In the strongly-coupled regime, their leading order reduces to the universal Arutyunov-Frolov-Staudacher phase as expected. We also compute their sub-leading order and compare it with recent one-loop perturbative results, and comment on their weak-coupling expansion.

This paper studies giant magnons in AdS 4 × 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.

We determine the off-shell symmetry algebra and representations of Type IIB superstring theory on AdS 3 × S 3 × T 4 with mixed R-R and NS-NS three-form flux. We use these to derive the non-perturbative worldsheet S matrix of fundamental excitations of the superstring theory. Our analysis includes both massive and massless modes and shows how turning on mixed three-form flux results in an integrable deformation of the S matrix of the pure R-R theory.

Integrability is believed to underlie the AdS 3 /CFT 2 correspondence with sixteen supercharges. We elucidate the role of massless modes within this integrable framework. Firstly, we find the dressing factors that enter the massless and mixed-mass worldsheet S matrix. Secondly, we derive a set of all-loop Bethe Equations for the closed strings, determine their symmetries and weak-coupling limit. Thirdly, we investigate the underlying Yangian symmetry in the massless sector and show that it fits into the general framework of Yangian integrability. In addition, we compare our S matrix in the near-relativistic limit with recent perturbative worldsheet calculations of Sundin and Wulff.

This is the published version of the paper.This version of the publication may differ from the final published version. We obtain the all-loop worldsheet S matrix for fundamental excitations on AdS 3 × S 3 × T 4 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 AdS 3 =CFT 2 integrability. Permanent repository link