Bethe Ansatz and the Spectral Theory of Affine Lie Algebra-Valued Connections I. The simply-laced Case

2015/01/31 by Davide Masoero, Andrea Raimondo, Daniele Valeri · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Ansatz #Bethe ansatz #Computer science #Integrable system #Lie algebra #Lie conformal algebra #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Ode #Pure mathematics #Quadratic equation #Set (abstract data type) #hep-th #math-ph #math.MP #math.RT #msc:17B67 #msc:34M40 #msc:37K30 #msc:82B23

paper · pdf · doi:10.1007/s00220-016-2643-6

published as Communications in Mathematical Physics, 344(3), 719-750, 2016 · 27 pages, final and published version. Minor change in the title

openalex publication_date 2016/05/19 · arxiv created 2016/06/16 · arxiv updated 2016/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the ODE/IM correspondence for ODE associated to \mathfrak g-valued connections, for a simply-laced Lie algebra \mathfrak g. We prove that subdominant solutions to the ODE defined in different fundamental representations satisfy a set of quadratic equations called Ψ-system. This allows us to show that the generalized spectral determinants satisfy the Bethe Ansatz equations.

Citations

• Spectral Determinants for Schrödinger Equation and Q-Operators of Conformal Field Theory
• The Bethe ansatz and the Tzitzéica–Bullough–Dodd equation
• Wall-crossing, Hitchin systems, and the WKB approximation
• Simple Lie algebras and topological ODEs
• Bethe Ansatz and the Spectral Theory of Affine Lie algebra–Valued Connections II: The Non Simply–Laced Case

Cited by

• The KdV vacuum operator and its Katz extension
• Bethe Ansatz and the Spectral Theory of Affine Lie algebra–Valued Connections II: The Non Simply–Laced Case