Spontaneous Supersymmetry Breaking and Nambu-Goldstone Modes in Interacting Majorana Chains

TL;DR

This paper explores spontaneous supersymmetry breaking and the emergence of Nambu-Goldstone modes in interacting Majorana chains, providing insights into non-relativistic SUSY phenomena.

Contribution

It introduces models of interacting Majorana chains with supersymmetry and analyzes their spontaneous SUSY breaking and associated NG modes.

Findings

Identification of spontaneous SUSY breaking in Majorana chains

Characterization of Nambu-Goldstone modes in non-relativistic systems

Insights into fermionic excitations arising from SUSY breaking

Abstract

In modern physics, spontaneous symmetry breaking is one of the most important and ubiquitous ideas. It is well known that the breakdown of global and continuous symmetry gives rise to gapless excitations called Nambu-Goldstone (NG) bosons. This is called NG theorem. Since the generators of broken symmetries are bosonic, the excitations are also bosons. On the other hand, excitations are thought of as fermionic when a generator of broken symmetry is fermionic. The most famous example of fermionic symmetry is supersymmetry (SUSY). SUSY is a symmetry that exchanges bosons and fermions. In high-energy physics, it is known that spontaneous SUSY breaking gives rise to massless modes called NG fermions or Nambu- Goldstinos. In non-relativistic systems, fewer examples of models with SUSY are studied. Therefore, spontaneous SUSY breaking in non-relativistic systems is less understood than that in nonrelativistic systems or spontaneous symmetry breaking. In this thesis, we introduce interacting Majorana models with supersymmetry (SUSY) and discuss the properties in terms of spontaneous SUSY breaking and NG modes.