Lattice Study of the O(3) Supersymmetric Sigma Model

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 su-persymmetry 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.

Deconstruction and Other Approaches to Supersymmetric Lattice Field Theories

“…The nonlinear symmetries of the 2d sigma model are important to the renormalizability of the theory, so sacrificing them could create severe problems with the continuum limit. Encouraging analytic results and some Monte Carlo simulations of the CP 1 model have been reported in [48,49].…”

“…Thus the counterterm corresponding to O p,α at the ℓth order in perturbation theory has UV degree D = −p + − 2ℓ. Operators that will survive in the continuum limit thus satisfy 49) corresponding to counterterms with UV degree D ≥ 0. On the other hand, in perturbation theory O p,α will consist of monomials of the elementary fields and spacetime derivatives of them.…”

Compact gauge fields for supersymmetric lattices

“…This led to the construction of the two dimensional Wess-Zumino and supersymmetric sigma models in various dimensions. [14,15] In [16], the general criteria under which a nilpotent symmetry can be carried consistently with a latticization had been analyzed(also see [17,18], which advocates more, and [19] for the recent results on N = 1 Wess-Zumino in d = 4). Recently, Sugino [20][21][22] generalized this approach to the gauge theories with compact gauge fields in the formulation.…”

Advances and applications of lattice supersymmetry

“…A superfield formulation was subsequently given in [7], where renormalization was discussed on symmetry and dimensional grounds. Whereas that study showed that radiative generation of supersymmetry violation in the continuum limit is not forbidden by lattice symmetries and dimensional arguments, recent Monte Carlo data seems to indicate no need for supersymmetry-restoring CTs [60,61].…”