Witten index and phase diagram of compactified N=1 supersymmetric Yang-Mills theory on the lattice

TL;DR

This paper investigates the phase structure of compactified N=1 supersymmetric Yang-Mills theory on the lattice, using the Witten index to test supersymmetry restoration and confinement persistence through non-perturbative Monte Carlo simulations.

Contribution

It provides the first non-perturbative lattice evidence supporting supersymmetry restoration and confinement in compactified N=1 SYM at low energies.

Findings

Disappearance of the deconfinement transition in the supersymmetric limit

Restoration of supersymmetry at low energies

Support for confinement persistence with periodic boundary conditions

Abstract

Owing to confinement, the fundamental particles of N=1 Supersymmetric Yang-Mills (SYM) theory, gluons and gluinos, appear only in colourless bound states at zero temperature. Compactifying the Euclidean time dimension with periodic boundary conditions for fermions preserves supersymmetry, and confinement is predicted to persist independently of the length of the compactified dimension. This scenario can be tested non-perturbatively with Monte-Carlo simulations on a lattice. SUSY is, however, broken on the lattice and can be recovered only in the continuum limit. The partition function of compactified N=1 SYM theory with periodic fermion boundary conditions corresponds to the Witten index. Therefore it can be used to test whether supersymmetry is realized on the lattice. Results of our recent numerical simulations are presented, supporting the disappearance of the deconfinement transition in the supersymmetric limit and the restoration of SUSY at low energies.