arXiv subjects

Shutaro Shimamura

Publications and source records attributed to Shutaro Shimamura.

5 recordsLinked to original sources

arXiv2026

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

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.

cond-mat.str-el↗

arXiv2025

On anomalies and fermionic unitary operators

We point out that fermionic unitary operators which anticommute among themselves appear in various situations in quantum field theories with anomalies in the Hamiltonian formalism. To illustrate, we give multiple derivations of the fact that position-dependent $U(1)$ transformations of two-dimensional theories with $U(1)$ symmetry of odd level are fermionic when the winding number is odd. We then relate this mechanism to the anomalies of the discrete $\mathbb{Z}_N \subset U(1)$ symmetry, whose description also crucially uses unitary operators which are fermionic. We also show that position-dependent $SU(2)$ transformations of four-dimensional theories with $SU(2)$ symmetry with Witten anomaly are fermionic and anticommute among themselves when the winding number is odd.

hep-th↗

arXiv2025

Gapless Foliated-Exotic Duality

In this work, we construct a new foliated quantum field theory equivalent to the exotic $\phi$-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 $\phi$-theories. Furthermore, we also investigate the foliated-exotic duality in the $\hat\phi$-theory, which is dual to the $\phi$-theory, and construct the foliated $\hat\phi$-theory. These are the first examples of the foliated-exotic duality in gapless theories.

cond-mat.str-el↗

arXiv2024

Anomaly of Subsystem Symmetries in Exotic and Foliated $BF$ Theories

We study the mixed 't Hooft anomaly of the subsystem symmetries in the exotic $BF$ theory and the foliated $BF$ theory in 2+1 dimensions, both of which are fractonic quantum field theories describing the equivalent physics. In the anomaly inflow mechanism, the 't Hooft anomaly of the subsystem symmetries can be canceled by combining a subsystem symmetry-protected topological (SSPT) phase in one dimension higher. In this work, we construct the exotic and foliated $BF$ theories with background gauge fields, and the exotic and foliated forms of the SSPT phases using the foliated-exotic duality. In the foliated form, we see that the non-topological defect that describes a fracton can be viewed as a symmetry-like operator. We also newly construct the foliated and exotic SSPT phases with different foliation structures via the foliated-exotic duality. We can show that the SSPT phases with different foliation structures cancel the same anomaly. This may provide a clue to the characterization of the 't Hooft anomaly of subsystem symmetries.

cond-mat.str-el↗

arXiv2023

Foliated-Exotic Duality in Fractonic BF Theories

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.

hep-th↗