Foliated-Exotic Duality in Fractonic BF Theories

Abstract

There has been proposed two continuum descriptions of fracton systems: foliated quantum field theories (FQFTs) and exotic quantum field theories. Certain fracton systems are believed to admit descriptions by both, and hence a duality is expected between such a class of FQFTs and exotic QFTs. In this paper we study this duality in detail for concrete examples in $2+1$ and $3+1$ dimensions. In the examples, both sides of the continuum theories are of $BF$-type, and we find the explicit correspondences of gauge-invariant operators, gauge fields, parameters, and allowed singularities and discontinuities. This deepens the understanding of dualities in fractonic quantum field theories.

46 pages

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Cited by in corpus (11)

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• Multipole and fracton topological order via gauging foliated SPT phases
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Exotic theta terms in 2+1d fractonic field theory