The 1+1D 𝒩=2 Wess--Zumino model
Abstract
We develop the 1+1D 𝒩=2 Wess--Zumino model with a central extension, starting from Wigner's theorem and the supertranslation group. The unitary representations of the group leads to the SUSY algebra of the generators and an extension of the group to include a central charge Z. We then derive a general boson/fermion mass-degeneracy theorem and construct the covariant derivative and a candidate action realizing this algebra, first for the vacuum (Z=0) sector and then for Z≠0, where the central extension's own coordinate ξ is treated explicitly. Compactifying ξ gives a Kaluza--Klein tower of massive multiplets with quantized central charge, while the kink survives intact as the tower's zero mode, saturating the general BPS bound M≥|Z| derived along the way. This is a pedagogical re-derivation, aimed at a reader's first encounter with these ideas, not a new result.
Related
- Revisiting the Wess-Zumino-Witten Term in Nuclear and Quark Matter under Magnetic Fields and Rotation
- Accessing the Wess-Zumino-Witten term using Lattice QCD
- Fractional Superfluid Vortices and Worldsheet Wess--Zumino--Witten Models in Two-Color QCD and Sp(2N) Gauge Theories
- The Wess-Zumino Action of the Conformal Anomaly
BibTeX
@misc{dawson2026𝒩2,
title = {{The 1+1D $\mathcalN=2$ Wess--Zumino model}},
author = {John F. Dawson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28832},
eprint = {2610.28832},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28832},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The 1+1D 𝒩=2 Wess--Zumino model
AU - John F. Dawson
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28832
UR - https://arxiv.org/abs/2610.28832
AB - We develop the 1+1D 𝒩=2 Wess--Zumino model with a central extension, starting from Wigner's theorem and the supertranslation group. The unitary representations of the group leads to the SUSY algebra of the generators and an extension of the group to include a central charge Z. We then derive a general boson/fermion mass-degeneracy theorem and construct the covariant derivative and a candidate action realizing this algebra, first for the vacuum (Z=0) sector and then for Z≠0, where the central extension's own coordinate ξ is treated explicitly. Compactifying ξ gives a Kaluza--Klein tower of massive multiplets with quantized central charge, while the kink survives intact as the tower's zero mode, saturating the general BPS bound M≥|Z| derived along the way. This is a pedagogical re-derivation, aimed at a reader's first encounter with these ideas, not a new result.
ER -