2012/07/31 by Raphael Flore, Daniel Körner, Andreas Wipf +1 · 13 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Lattice (music) #Mathematical physics #Nonlinear Waves and Solitons #Nonlinear model #Nonlinear system #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Sigma #Sigma model #Statistical physics #hep-lat #hep-th
paper · pdf · doi:10.1007/jhep11(2012)159
published in Journal of High Energy Physics 2012(11) (Springer Nature) · 35 pages, 36 figures, 2 tables; updated version as accepted by JHEP
openalex publication_date 2012/11/01 · arxiv created 2013/05/07 · arxiv updated 2013/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A supersymmetric extension of the nonlinear O(3) sigma model in two spacetime dimensions is investigated by means of Monte Carlo simulations. We argue that it is impossible to construct a lattice action that implements both the O(3) symmetry as well as at least one supersymmetry exactly at finite lattice spacing. It is shown by explicit calculations that previously proposed discretizations fail to reproduce the exact symmetries of the target manifold in the continuum limit. We provide an alternative lattice action with exact O(3) symmetry and compare two approaches based on different derivative operators. Using the nonlocal SLAC derivative for the quenched model on moderately sized lattices we extract the value σ(2, u0) = 1.2604(13) for the step scaling function at u0 = 1.0595, to be compared with the exact value 1.261210. For the supersymmetric model with SLAC derivative the discrete chiral symmetry is maintained but we encounter strong sign fluctuations, rendering large lattice simulations ineffective. By applying the Wilson prescription, supersymmetry and chiral symmetry are broken explicitly at finite lattice spacing, though there is clear evidence that both are restored in the continuum limit by fine tuning of a single mass parameter.