Norms and scalar products for AdS₃

2019/11/15 by Juan Miguel Nieto, Nieto, Juan Miguel, Алессандро Торриелли +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.1911.06590

openalex publication_date 2019/11/15 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28

Abstract

We compute scalar products and norms of Bethe vectors in the massless sector of AdS₃ 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 AdS₃ S-matrix theory.

Citations

• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• The \AdS₃\× \S³\×\n \S³\×\S¹ worldsheet S matrix
• The plane-wave limit of \rm AdS₃ × \rm S³ × \rm S³ × \rm S¹

Cited by

• Boundary Bethe ansatz in massive AdS₃

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