Foliated-Exotic Duality and Anomaly Inflow in Fracton Quantum Field Theories

TL;DR

This paper explores the duality between exotic and foliated quantum field theories in fracton phases, extending it with anomaly inflow to connect gapped and gapless theories and revealing new dualities involving subsystem symmetries.

Contribution

It extends the foliated-exotic duality to include anomaly inflow, establishing new correspondences in both gapped and gapless fracton theories with subsystem symmetries.

Findings

Established the foliated-exotic duality in 2+1D fractonic $BF$ theories with $ ext{Z}_N imes ext{Z}_N$ symmetry.

Constructed the foliated description of SSPT phases related to these dualities.

First example of foliated-exotic duality applied to a gapless fractonic scalar field theory.

Abstract

Fracton phases are new types of phases of matter characterized by subsystem global symmetry, which is a generalized global symmetry whose symmetry operator is partially topological. Their continuum low-energy effective descriptions admit two different formulations: an exotic quantum field theory (QFT) using exotic tensor gauge fields, and a foliated QFT constructed from a foliation structure and foliated gauge fields. For certain fracton QFTs, these two descriptions are equivalent, which is called the foliated-exotic duality. In this dissertation, we extend the foliated-exotic duality by combining it with the anomaly inflow mechanism for 't Hooft anomalies of subsystem symmetries. This dissertation has two main results. First, we discuss the exotic and foliated $BF$ theories in 2+1 dimensions, which exhibit the mixed 't Hooft anomaly of $\mathbb{Z}_N \times \mathbb{Z}_N$ subsystem symmetry. This anomaly is captured by a subsystem symmetry-protected topological (SSPT) phase for $\mathbb{Z}_N \times \mathbb{Z}_N$ subsystem symmetry in one dimension higher. By extending the foliated-exotic duality in the fractonic $BF$ theory to the SSPT phase, we establish the field correspondences in the SSPT phase and construct the foliated description of the SSPT phase. Second, we discuss the exotic $\phi$-theory in 2+1 dimensions -- a fractonic gapless scalar field theory, which has the 't Hooft anomaly of $U(1) \times U(1)$ subsystem symmetry. The anomaly is captured by an SSPT phase for $U(1) \times U(1)$ subsystem symmetry in 3+1 dimensions via the anomaly inflow mechanism. Extending the foliated-exotic duality to the $\phi$-theory, we establish field correspondences in the $\phi$-theory and construct the foliated $\phi$-theory that is equivalent to the exotic $\phi$-theory. This provides the first example of the foliated-exotic duality in gapless theories.