Towards the All-Loop WorldsheetSMatrix forAdS3×S3×T

Abstract

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

Integrability and the conformal field theory of the Higgs branch

“…This is the first appearance of integrability on the CFT 2 side of the duality. Together with the evidence for integrability that has been found on the string theory side [11][12][13][14], it provides a powerful argument for a holographic integrability description of AdS 3 /CFT 2 . This evidence leads us to suggest that the perturbative closed strings of the R-R AdS 3 background are dual to CFT 2 states localised near the small-instanton singularity.…”

“…The excitations fit perfectly in the massless psu(1|1) 4 c.e. ⊕ su(2) • representation discussed in [11,12]. While the operators containing these fields form reducible short representations at tree-level, we expect them to join into long irreducible representations once we include the interactions.…”

“…The Lagrangian for the fundamental hypermultiplet and its couplings to the vector multiplet then takes the form 11) and the Lagrangian for the adjoint hypermultiplet the form…”

“…In previous works [11,18,21,22], we have constructed an integrable worldsheet S matrix which can be used to calculate the perturbative closed string spectrum to all orders in the string tension on the AdS 3 side. Using this construction, the weakly-coupled spin-chain limit of the integrable system was obtained [18,22].…”

“…Superstrings on AdS 3 backgrounds with 16 supersymmetries are known to be classically integrable [6][7][8], and so one may wonder whether integrability underlies the AdS 3 /CFT 2 correspondence. 1 Recently, we have found the complete non-perturbative world-sheet integrable S matrix of string theory on such AdS 3 backgrounds, including the hitherto unaccounted for massless modes [11][12][13][14]. 2 It appears now very likely that the AdS 3 /CFT 2 correspondence with 16…”