Supersymmetric Nonlinear O(3) Sigma Model on the Lattice

Understand

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.