String membrane nets from higher-form gauging: An alternate route to 𝑝-string condensation

Journal Article · Thu Sep 11 00:00:00 EDT 2025 · Physical Review. B

DOI:https://doi.org/10.1103/qq9n-16hk· OSTI ID:2873256

Gorantla, Pranay ^[1]; Prem, Abhinav ^[2]; Tantivasadakarn, Nathanan ^[3]; Williamson, Dominic J. ^[4]

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1. University of Chicago, IL (United States); Princeton University, NJ (United States)
2. Institute for Advanced Study, Princeton, NJ (United States); Bard College, Annandale-On-Hudson, NY (United States)
3. California Institute of Technology (CalTech), Pasadena, CA (United States)
4. The University of Sydney, NSW (Australia)

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.

• Research Organization: Institute for Advanced Study, Princeton, NJ (United States)
• Sponsoring Organization: Australian Research Council Discovery Early Career Research; National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0009988
• OSTI ID: 2873256
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 12 Vol. 112; ISSN 2469-9969; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

Anyons
Effective field theory
Fractons
Strongly correlated systems
Symmetries in condensed matter
Topological phases of matter