Proliferation transitions from a topological phase in $2+1$ dimensions

Fuente: arXiv
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Main Authors: Cheng, Meng, Seiberg, Nathan
Format: Preprint
Published: 2026
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author Cheng, Meng
Seiberg, Nathan
author_facet Cheng, Meng
Seiberg, Nathan
contents We consider phase transitions out of a general topological phase in $2+1$ dimensions. We assume that the transition is triggered by a single Abelian anyon, which becomes light near the transition and whose worldlines proliferate after the transition. (This proliferation is often referred to as ``condensation.'') We describe the transition using a continuum field theory obtained by coupling the corresponding topological quantum field theory (TQFT) to a single complex scalar field associated with this anyon. With these assumptions, we find the most general relativistic field theory for such a transition. Even though for a given TQFT and a choice of anyon, there are infinitely many such field theories, the transition theory depends on only a single additional integer parameter. We analyze all these theories, their global symmetries, and their phases. In generic cases, the theory after the transition can be related to the original one via an Abelian hierarchy construction. In special cases, the theory after the transition is gapless, and with a particular deformation, it is related to the original TQFT by gauging an anomaly-free one-form global symmetry. We also explore the enrichment of this setup by a global U(1) symmetry. In some cases, enriching the original TQFT is incompatible with the full transition theory. Finally, we demonstrate our construction with many specific examples.
format Preprint
id arxiv_https___arxiv_org_abs_2603_00245
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Proliferation transitions from a topological phase in $2+1$ dimensions
Cheng, Meng
Seiberg, Nathan
Strongly Correlated Electrons
High Energy Physics - Theory
We consider phase transitions out of a general topological phase in $2+1$ dimensions. We assume that the transition is triggered by a single Abelian anyon, which becomes light near the transition and whose worldlines proliferate after the transition. (This proliferation is often referred to as ``condensation.'') We describe the transition using a continuum field theory obtained by coupling the corresponding topological quantum field theory (TQFT) to a single complex scalar field associated with this anyon. With these assumptions, we find the most general relativistic field theory for such a transition. Even though for a given TQFT and a choice of anyon, there are infinitely many such field theories, the transition theory depends on only a single additional integer parameter. We analyze all these theories, their global symmetries, and their phases. In generic cases, the theory after the transition can be related to the original one via an Abelian hierarchy construction. In special cases, the theory after the transition is gapless, and with a particular deformation, it is related to the original TQFT by gauging an anomaly-free one-form global symmetry. We also explore the enrichment of this setup by a global U(1) symmetry. In some cases, enriching the original TQFT is incompatible with the full transition theory. Finally, we demonstrate our construction with many specific examples.
title Proliferation transitions from a topological phase in $2+1$ dimensions
topic Strongly Correlated Electrons
High Energy Physics - Theory
url https://arxiv.org/abs/2603.00245