Supercurrents and Brane Currents in Diverse Dimensions

TL;DR

This paper classifies supersymmetry multiplets containing currents across various dimensions, revealing their role in brane charges and implications for supersymmetric field theory dynamics.

Contribution

It systematically analyzes supersymmetry multiplets with currents, introducing the S-multiplet and its decompositions, and explores their physical implications for brane charges and supersymmetry breaking.

Findings

Identifies the S-multiplet as the most general supersymmetry current multiplet.

Shows the S-multiplet's relevance for string and domain wall charges.

Derives constraints on charged branes and magnetic charges in specific theories.

Abstract

We systematically analyze all possible supersymmetry multiplets that include the supersymmetry current and the energy-momentum tensor in various dimensions, focusing on N=1 in four dimensions. The most general such multiplet is the S-multiplet, which includes 16 bosonic and 16 fermionic operators. In special situations it can be decomposed, leading to smaller multiplets with 12+12 or even 8+8 operators. Physically, these multiplets give rise to different brane charges in the supersymmetry algebra. The S-multiplet is needed when the algebra contains both string and domain wall charges. In lower dimensions (or in four-dimensional N=2 theories) the algebra can include space-filling brane charges, which are associated with partial supersymmetry breaking. This phenomenon is physically distinct from ordinary spontaneous supersymmetry breaking. Our analysis leads to new results about the dynamics of supersymmetric field theories. These include constraints on the existence of certain charged branes and the absence of magnetic charges in U(1) gauge theories with a Fayet-Iliopoulos term.