Supersymmetry Breaking in Low Dimensional Models

TL;DR

This paper investigates supersymmetry breaking in low-dimensional models using lattice methods, comparing results with exact approaches, and provides new insights into the phase structure and critical couplings of these models.

Contribution

It demonstrates the effectiveness of lattice methods, especially with the SLAC derivative, in studying supersymmetry breaking and presents the first computation of a renormalized critical coupling in the 2D supersymmetric model.

Findings

Lattice methods accurately reproduce physical properties of supersymmetric quantum mechanics.

The SLAC derivative is suitable for quenched 2D phi^4 models.

First renormalized critical coupling computed for the 2D supersymmetric model.

Abstract

We analyse supersymmetric models that show supersymmetry breaking in one and two dimensions using lattice methods. Starting from supersymmetric quantum mechanics we explain the fundamental principles and problems that arise in putting supersymmetric models onto the lattice. We compare our lattice results (built upon the non-local SLAC derivative) with numerically exact results obtained within the Hamiltonian approach. A particular emphasis is put on the discussion of boundary conditions. We investigate the ground state structure, mass spectrum, effective potential and Ward identities and conclude that lattice methods are suitable to derive the physical properties of supersymmetric quantum mechanics, even with broken supersymmetry. Based on this result we analyse the two dimensional N=1 Wess-Zumino model with spontaneous supersymmetry breaking. First we show that (in agreement with earlier analytical and numerical studies) the SLAC derivative is a sensible choice in the quenched model, which is nothing but the two dimensional phi^4 model. Then, we present the very first computation of a renormalised critical coupling for the complete supersymmetric model. This calculation makes use of Binder cumulants and is supported by a direct comparison to Ward identity results, both in the continuum and infinite volume limit. The physical picture is completed by masses at two selected couplings, one in the supersymmetric phase and one in the supersymmetry broken phase. Signatures of the Goldstino in the fermionic correlator are clearly visible in the broken case.