2015/09/30 by Ben Hoare, Antonio Pittelli, Алессандро Торриелли +1 · 22 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Ansatz #Bethe ansatz #Black Holes and Theoretical Physics #Combinatorics #Integrable system #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Superstring theory #Supersymmetry #Yangian #hep-th
paper · pdf · doi:10.1103/physrevd.93.066006
published in Physical review. D/Physical review. D. 93(6) (American Physical Society) · 27 pages, no figures; Version to appear in Phys. Rev. D
arxiv created 2016/03/10 · openalex publication_date 2016/03/18 · arxiv updated 2016/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper, we find the Yangian algebra responsible for the integrability of the AdS2\ifmmode×\else\texttimes\fiS2\ifmmode×\else\texttimes\fiT6 superstring in the planar limit. We demonstrate the symmetry of the corresponding exact S matrix in the massive sector, including the presence of the secret symmetry. We give two alternative presentations of the Hopf algebra. The first takes the usual canonical form, which, as the relevant representations are long, leads to a Yangian representation that is not of evaluation type. After investigating the relationship between cocommutativity, evaluation representations and the shortening condition, we find an alternative realization of the Yangian whose representation is of the evaluation type. Finally, we explore two limits of the S matrix. The first is the classical r matrix, where we rediscover the need for a secret symmetry also in this context. The second is the simplifying zero-coupling limit. In this limit, taking the S matrix as a generating R matrix for the algebraic Bethe ansatz, we obtain an effective model of free fermions on a periodic spin-chain. This limit should provide hints to the one-loop anomalous dimension of the mysterious superconformal quantum mechanics dual to the superstring theory in this geometry.