String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation

• URL: http://arxiv.org/abs/2505.13604v1
• Date: Mon, 19 May 2025 18:00:04 GMT
• Title: String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Authors: Pranay Gorantla, Abhinav Prem, Nathanan Tantivasadakarn, Dominic J. Williamson,
• Abstract summary: We show that gauging a 1-form symmetry in 3+1D that is generated by Abelian anyons in isotropic stacks of 2+1D topological orders naturally results in a 3+1D $p$-string condensed phase.<n>This approach clarifies the symmetry principles underlying $p$-string condensation and generalizes the familiar connection between anyon condensation and one-form gauging.
• Score: 0.12499537119440243
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a new perspective on the $p$-string condensation procedure for constructing 3+1D fracton phases by implementing this process via the gauging of higher-form symmetries. Specifically, we show that gauging a 1-form symmetry in 3+1D that is generated by Abelian anyons in isotropic stacks of 2+1D topological orders naturally results in a 3+1D $p$-string condensed phase, providing a controlled non-perturbative construction that realizes fracton orders. This approach clarifies the symmetry principles underlying $p$-string condensation and generalizes the familiar connection between anyon condensation and one-form gauging in two spatial dimensions. We demonstrate this correspondence explicitly in both field theories and lattice models: in field theory, we derive the foliated field theory description of the $\mathbb{Z}_N$ X-Cube model by gauging a higher-form symmetry in stacks of 2+1D $\mathbb{Z}_N$ gauge theories; on the lattice, we show how gauging a diagonal 1-form symmetry in isotropic stacks of $G$-graded string-net models leads to string-membrane-nets hosting restricted mobility excitations. This perspective naturally generalizes to spatial dimensions $d \geq 2$ and provides a step towards building an algebraic theory of $p$-string condensation.

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