Supersphere non-linear sigma model on the lattice

TL;DR

This paper explores a supersymmetric extension of the two-dimensional non-linear sigma model on the supersphere, discussing its theoretical properties, lattice discretization, and preliminary numerical simulation results.

Contribution

It introduces a lattice discretization and simulation strategy for the supersphere non-linear sigma model, extending known models to include supersymmetry.

Findings

Preliminary numerical results demonstrate the feasibility of simulating the supersphere model.

The model's renormalization properties are briefly characterized.

A strategy for numerical simulations on the lattice is proposed.

Abstract

Two-dimensional $O(N)$ non-linear sigma models are exactly solvable theories and have many applications, from statistical mechanics to their use as QCD toy models. We consider a supersymmetric extension, the non-linear sigma model on the supersphere~$S^{N+2m-1|2m}\equiv \frac{OSP(N+2m|2m)}{OSP(N+2m-1|2m)}$. We briefly describe its renormalization properties and lattice discretization, and present a strategy for numerical simulations together with some preliminary numerical results.