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Theory of oblique topological insulators

by Benjamin Moy, Hart Goldman, Ramanjit Sohal, Eduardo Fradkin

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Benjamin Moy
Submission information
Preprint Link: scipost_202209_00027v2  (pdf)
Date accepted: 2022-11-23
Date submitted: 2022-10-12 04:00
Submitted by: Moy, Benjamin
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI phases are characterized by fractional $\Theta$-angles, long-range entanglement, and fractionalization. Starting from a simple family of $\mathbb{Z}_N$ lattice gauge theories due to Cardy and Rabinovici, we develop a class of FTI phases based on the physical mechanism of oblique confinement and the modern language of generalized global symmetries. We dub these phases oblique topological insulators. Oblique TIs arise when dyons—bound states of electric charges and monopoles—condense, leading to FTI phases characterized by topological order, emergent one-form symmetries, and gapped boundary states not realizable in 2+1-D alone. Based on the lattice gauge theory, we present continuum topological quantum field theories (TQFTs) for oblique TI phases involving fluctuating one-form and two-form gauge fields. We show explicitly that these TQFTs capture both the generalized global symmetries and topological orders seen in the lattice gauge theory. We also demonstrate that these theories exhibit a universal "generalized magnetoelectric effect" in the presence of two-form background gauge fields. Moreover, we characterize the possible boundary topological orders of oblique TIs, finding a new set of boundary states not studied previously for these kinds of TQFTs.

Author comments upon resubmission

We thank the referees for their comments and questions, which have been useful in improving the clarity of the manuscript. We directly reply to the remaining question of Referee 1 using the "Reply to the above report" option.

List of changes

New paragraph at the end of Section 6 clarifying the response computed using the TQFT

Replaced Ref. [34] with the published version

Published as SciPost Phys. 14, 023 (2023)

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