Differential equations and duality in massless integrable field theories at zero temperature

1999/04/12 by Paul Fendley, P. Fendley, H. Saleur +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Duality (order theory) #Field (mathematics) #Integrable system #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Philosophy #Physics #Pure mathematics #Quantum electrodynamics #Quantum mechanics #Zero (linguistics) #Zero temperature #hep-th #nlin.SI #solv-int

paper · pdf · doi:10.1016/s0550-3213(99)00832-9

published as Nucl.Phys.B574:571-586,2000 · 18 pages, harvmac

arxiv created 1999/04/12 · openalex publication_date 2000/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Functional relations play a key role in the study of integrable models. We argue in this paper that for massless field theories at zero temperature, these relations can in fact be interpreted as monodromy relations. Combined with a recently discovered duality, this gives a way to bypass the Bethe ansatz, and compute directly physical quantities as solutions of a linear differential equation, or as integrals over a hyperelliptic curve. We illustrate these ideas in details in the case of the c=1 theory, and the associated boundary sine-Gordon model.

Citations

• Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
• Hyperelliptic curves for multichannel quantum wires and the multichannel Kondo problem
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• The generalized multi-channel Kondo model: Thermodynamics and fusion equations
• Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD