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 $C_2$ 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.