On gauge coupling constant in linearization of nonlinear supersymmetry

TL;DR

This paper investigates the relationship between N=2 supersymmetric QED and nonlinear SUSY models in two dimensions, revealing a mechanism that determines the gauge coupling constant from auxiliary field structures.

Contribution

It introduces a theoretical mechanism that determines the gauge coupling constant in N=2 SUSY QED through the structure of auxiliary fields in the linearization process.

Findings

The gauge coupling constant is determined by auxiliary field structures.

The nonlinear/linear SUSY relation constrains the electromagnetic coupling.

Explicit demonstration in two dimensions confirms the mechanism.

Abstract

We study in two space-time dimensions (d = 2) the relation between N = 2 supersymmetric (SUSY) QED theory and N = 2 nonlinear (NL) SUSY model by linearizing N = 2 NLSUSY generally based upon the fundamental notions of the basic theory. We find a remarkable mechanism which determines theoretically the magnitude of the bare gauge coupling constant from the general structure of auxiliary fields. We show explicitly in d = 2 that the NL/linear SUSY relation (i.e. a SUSY compositeness condition for all particles) determines the magnitude of the bare electromagnetic coupling constant (i.e. the fine structure constant) of N = 2 SUSY QED.