Norms and scalar products for AdS_3

Abstract

We compute scalar products and norms of Bethe vectors in the massless sector of AdS_3 integrable superstring theories, by exploiting the general difference form of the S-matrix of massless excitations in the pure Ramond-Ramond case, and the difference form valid only in the BMN limit in the mixed-flux case. We obtain determinant-like formulas for the scalar products, generalising a procedure developed in previous literature for standard R-matrices to the present non-conventional situation. We verify our expressions against explicit calculations using Bethe vectors for chains of small length, and perform some computer tests of the exact formulas as far as numerical accuracy sustains us. This should be the first step towards the derivation of integrable form-factors and correlation functions for the AdS_3 S-matrix theory.

32 pages, no figures; added reference

References in corpus (16)

• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
• $Ad{S}_3\times S^3\times M^4$ string S-matrices from unitarity cuts
• S-matrix for magnons in the D1-D5 system
• The Quantum Deformed Mirror TBA I
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• Macroscopic (and Microscopic) Massless Modes
• Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2)
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• D1 and D5-brane giant gravitons on $Ad{S}_3\times S^3\times S^3\times S^1$
• An improved AFS phase for AdS3 string integrability
• Isometry Group Orbit Quantization of Spinning Strings in AdS_3 x S^3