Supersymmetric Nonlinear O(3) Sigma Model on the Lattice

Abstract

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, u_0) = 1.2604(13) for the step scaling function at u_0 = 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.

35 pages, 36 figures, 2 tables; updated version as accepted by JHEP

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• A Theory of Dark Matter
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• Low-dimensional Supersymmetric Lattice Models
• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
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Cited by in corpus (9)

• Lectures on renormalization and asymptotic safety
• Quantum Monte Carlo simulation of the chiral Heisenberg Gross-Neveu-Yukawa phase transition with a single Dirac cone
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Critical flavour number of the Thirring model in three dimensions
• Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Generalized supersymmetry and sigma models
• Symmetries of Thirring models on 3d lattices
• $\mathcal{N}=1$ Super-Yang-Mills theory on the lattice with twisted mass fermions
• Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions