Moduli Space of Global Symmetry in N=1 Supersymmetric Theories and the Quasi-Nambu-Goldstone Bosons

TL;DR

This paper characterizes the moduli space of global symmetries in N=1 supersymmetric theories, highlighting the role of quasi-Nambu-Goldstone bosons and the structure of symmetry breaking points.

Contribution

It derives the moduli space structure, including the emergence of QNG bosons at singular points, and describes the low-energy effective Lagrangian as an arbitrary function of the orbit map.

Findings

Moduli space coincides with QNG bosons at generic points.

Singular points feature enhanced unbroken symmetry and NG to QNG boson transition.

Effective Lagrangian is an arbitrary function of the orbit map.

Abstract

We derive the moduli space for the global symmetry in N=1 supersymmetric theories. We show, at the generic points, it coincides with the space of quasi-Nambu-Goldstone (QNG) bosons, which appear besides the ordinary Nambu-Goldstone (NG) bosons when global symmetry G breaks down spontaneously to its subgroup H with preserving N=1 supersymmetry. At the singular points, most of the NG bosons change to the QNG bosons and the unbroken global symmetry is enhanced. The G-orbits parametrized by the NG bosons are the fibre at the moduli space and the singular points correspond to the point where H-orbit (in G-orbit) shrinks. We also show the low-energy effective Lagrangian is the arbitrary function of the orbit map.