Higher-Form Description of Chiral Soliton Lattice
Abstract
The chiral soliton lattice (CSL) is conventionally described as a periodic winding configuration of a compact scalar field. In this paper, we formulate the CSL in a higher-form framework based on a Stückelberg coupling between a two-form gauge field C2 and a three-form gauge field A3, in which strings and walls can be treated directly as extended sources. Higher-form gauge invariance requires the string worldsheet to be the boundary of the wall worldvolume. In the quadratic dual effective theory, exchange of the massive higher-form mode generates a repulsive Yukawa interaction between parallel walls. With its coefficient fixed by duality, the resulting CSL lattice spacing agrees well with the exact Sine--Gordon result without parameter fitting. We then extend the description to a nonlinear, multi-branch higher-form theory. It reproduces the exact dilute wall--wall interaction coefficient, the periodic CSL and its energy-minimization condition, as well as the gapless CSL phonon. The phonon is identified as a collective displacement of the periodic higher-form background, while scalar winding is reinterpreted as branch flow of the nonlinear higher-form theory.
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BibTeX
@misc{ookouchi2026higherform,
title = {{Higher-Form Description of Chiral Soliton Lattice}},
author = {Yutaka Ookouchi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32212},
eprint = {2609.32212},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32212},
}
RIS
TY - UNPB
TI - Higher-Form Description of Chiral Soliton Lattice
AU - Yutaka Ookouchi
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32212
UR - https://arxiv.org/abs/2609.32212
AB - The chiral soliton lattice (CSL) is conventionally described as a periodic winding configuration of a compact scalar field. In this paper, we formulate the CSL in a higher-form framework based on a Stückelberg coupling between a two-form gauge field C_2 and a three-form gauge field A_3, in which strings and walls can be treated directly as extended sources. Higher-form gauge invariance requires the string worldsheet to be the boundary of the wall worldvolume. In the quadratic dual effective theory, exchange of the massive higher-form mode generates a repulsive Yukawa interaction between parallel walls. With its coefficient fixed by duality, the resulting CSL lattice spacing agrees well with the exact Sine--Gordon result without parameter fitting. We then extend the description to a nonlinear, multi-branch higher-form theory. It reproduces the exact dilute wall--wall interaction coefficient, the periodic CSL and its energy-minimization condition, as well as the gapless CSL phonon. The phonon is identified as a collective displacement of the periodic higher-form background, while scalar winding is reinterpreted as branch flow of the nonlinear higher-form theory.
ER -