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Gapless Foliated-Exotic Duality

Kantaro Ohmori, Shutaro Shimamura

Abstract

In this work, we construct a new foliated quantum field theory equivalent to the exotic $φ$-theory -- a fractonic gapless scalar field theory described by tensor gauge fields and exhibiting $U(1) \times U(1)$ subsystem global symmetry. This subsystem symmetry has an 't Hooft anomaly, which is captured by a subsystem symmetry-protected topological (SSPT) phase in one dimension higher via the anomaly inflow mechanism. By analyzing both the anomaly inflow structure and the foliated-exotic duality in the SSPT phases, we establish the foliated-exotic duality in the $φ$-theories. Furthermore, we also investigate the foliated-exotic duality in the $\hatφ$-theory, which is dual to the $φ$-theory, and construct the foliated $\hatφ$-theory. These are the first examples of the foliated-exotic duality in gapless theories.

Gapless Foliated-Exotic Duality

Abstract

In this work, we construct a new foliated quantum field theory equivalent to the exotic -theory -- a fractonic gapless scalar field theory described by tensor gauge fields and exhibiting subsystem global symmetry. This subsystem symmetry has an 't Hooft anomaly, which is captured by a subsystem symmetry-protected topological (SSPT) phase in one dimension higher via the anomaly inflow mechanism. By analyzing both the anomaly inflow structure and the foliated-exotic duality in the SSPT phases, we establish the foliated-exotic duality in the -theories. Furthermore, we also investigate the foliated-exotic duality in the -theory, which is dual to the -theory, and construct the foliated -theory. These are the first examples of the foliated-exotic duality in gapless theories.

Paper Structure

This paper contains 22 sections, 242 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Note added:
  3. Exotic and Foliated SSPT Phase for U(1) × U(1) Subsystem Symmetry
  4. Exotic SSPT Phase in 3+1 Dimensions
  5. Exotic φ-Theory in 2+1 Dimensions
  6. Field Correspondences and Foliated SSPT Phase in 3+1 Dimensions
  7. Boundary Theory for Foliated SSPT Phase
  8. Construction of Boundary Theory
  9. Construction of Foliated φ-Theory
  10. Foliated-Exotic Duality in φ-Theory
  11. Duality and Foliated φhat-Theory
  12. Exotic φhat-Theory
  13. Construction of Foliated φhat-Theory
  14. Foliated-Exotic Duality in φhat-Theory
  15. Duality in Foliated phi-Theory
  16. ...and 7 more sections

Figures (1)

  • Figure 1: The structure of the anomaly inflow and dualities.