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SymTFT construction of gapless exotic-foliated dual models

Fabio Apruzzi, Francesco Bedogna, Salvo Mancani

Abstract

We construct Symmetry Topological Field Theories (SymTFTs) for continuous subsystem symmetries, which are inherently non-Lorentz-invariant. Our framework produces dual bulk descriptions -- gapped foliated and exotic SymTFTs -- that generate gapless boundary theories with spontaneous subsystem symmetry breaking via interval compactification. In analogy with the sandwich construction of SymTFT, we call this Mille-feuille. This is done by specifying gapped and symmetry-breaking boundary conditions. In this way we obtain the foliated dual realizations of various models, including the XY plaquette, XYZ cube, and $φ$, $\hatφ$ theories. This also captures self-duality symmetries as condensation defects and provides a systematic method for generating free theories that non-linearly realize subsystem symmetries.

SymTFT construction of gapless exotic-foliated dual models

Abstract

We construct Symmetry Topological Field Theories (SymTFTs) for continuous subsystem symmetries, which are inherently non-Lorentz-invariant. Our framework produces dual bulk descriptions -- gapped foliated and exotic SymTFTs -- that generate gapless boundary theories with spontaneous subsystem symmetry breaking via interval compactification. In analogy with the sandwich construction of SymTFT, we call this Mille-feuille. This is done by specifying gapped and symmetry-breaking boundary conditions. In this way we obtain the foliated dual realizations of various models, including the XY plaquette, XYZ cube, and , theories. This also captures self-duality symmetries as condensation defects and provides a systematic method for generating free theories that non-linearly realize subsystem symmetries.

Paper Structure

This paper contains 34 sections, 138 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Note added:
  3. SymTFT for continuous abelian symmetries and SSB
  4. Sandwich construction with conformal boundary condition
  5. Continuous subsystem symmetries
  6. XY-plaquette model
  7. XYZ-cube model
  8. $\phi$-model
  9. $\hat{\phi}$-model
  10. Exotic and foliated SymTFTs, gapless models and dualities
  11. XY-plaquette model
  12. Exotic-foliated interfaces
  13. XYZ-cube model
  14. Exotic SymTFT
  15. Foliated SymTFT
  16. ...and 19 more sections

Figures (3)

  • Figure 1: The Mille-feuille. The vertical direction is the foliated one. Some defects of the theory will be topological only on the green layer plane.
  • Figure 2: A strip $\Tilde{U}$ linking a point operator $V$ on a 2 dimensional submanifold.
  • Figure 3: The interface $S_I$ that implements the duality map between foliated and exotic theories.