Dynamical Breaking of Supersymmetry in Noncommutative Gauge Theories

TL;DR

This paper introduces a novel mechanism for spontaneous supersymmetry breaking in noncommutative gauge theories, where IR/UV mixing induces gauge symmetry breaking and decoupling of U(1) sectors, with potential implications for string theory.

Contribution

It demonstrates that noncommutative gauge theories can spontaneously break supersymmetry and gauge invariance via IR/UV mixing, with a natural Fayet-Iliopoulos term leading to a decoupled U(1) sector.

Findings

Supersymmetry is spontaneously broken by a Fayet-Iliopoulos D-term.

Gauge symmetry breaks from U(n) to U(1) x SU(n) at low energies.

U(1) degrees of freedom become weakly coupled and decouple in the IR.

Abstract

We propose a new mechanism of spontaneous supersymmetry breaking in noncommutative gauge theories. We find that in N=1 noncommutative gauge theories both supersymmetry and gauge invariance are dynamically broken. Supersymmetry is broken spontaneously by a Fayet-Iliopoulos D-term which naturally arises in a noncommutative U(n) theory. For a non-chiral matter content the Fayet-Iliopoulos term is not renormalized and its tree-level value can be chosen to be much smaller than the relevant string/noncommutativity scale. In the low energy theory, the noncommutative U(n) gauge symmetry is broken down to a commutative U(1) x SU(n). This breaking is triggered by the IR/UV mixing and manifests itself at and below the noncommutativity mass scale M_{NC}\sim \theta^{-1/2}. In particular, the U(1) degrees of freedom decouple from the SU(n) in the infrared and become arbitrarily weakly coupled, thus playing the role of the hidden sector for supersymmetry breaking.