Toolkit for general 2d scalar potential in LCT

• Published in: The journal of high energy physics Vol. 2025; no. 6; pp. 193 - 30
• Main Authors: Fitzpatrick, A. Liam, Katz, Emanuel, Xin, Yuan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 19.06.2025; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Classical and Quantum Gravitation; Elementary Particles; Fermions; Field Theories in Lower Dimensions; Fourier transforms; Nonperturbative Effects; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scalars; String Theory; Field Theories in Lower Dimensions; Nonperturbative Effects
• ISSN: 1029-8479; 1126-6708; 1127-2236; 1029-8479
• DOI: 10.1007/JHEP06(2025)193

A bstract We present efficient algorithms for obtaining the Hamiltonian in Lightcone Conformal Truncation (LCT) for a 2d scalar field with a generic potential. We apply this method to the sine-Gordon and sinh-Gordon models in 1 +1 d , and find precise agreement with integrability results when the scaling dimension ∆ of the deforming cosine/cosinh potential is in the range ∆ ≤ 1. The agreement provides additional evidence for a recent conjecture for how to compute the effective lightcone Hamiltonian in this class of models. In addition, to high precision, we provide the first direct confirmation for the conjectured self-duality of the sinh-Gordon model (∆ < 0), which relates ∆ ↔ 4/∆. As the dimension approaches the upper limit ∆ = 1 from below, we show analytically that the Hamiltonian matrix elements exactly reproduce those of a free Majorana fermion, demonstrating how bosonization is manifested in the LCT basis. We comment on the possible extension of the approach to ∆ > 1.