Explanipedia

Haagerup Symmetry in $(E_8)_1$? Open

Jan Albert, Yamato Honda, Justin Kaidi, Yunqin Zheng · 2025

We suggest that the chiral $(\mathfrak{e}_8)_1$ theory -- in many senses the simplest VOA -- may have Haagerup symmetry $\mathcal{H}_i$ for $i=1,2,3$. Likewise, we suggest that the non-chiral $(E_8)_1$ WZW model may have $\mathcal{H}_i \ti…

Non-local conserved currents and continuous non-invertible symmetries Open

Diego Delmastro, Adar Sharon, Yunqin Zheng · 2025

A bstract We embark on a systematic study of continuous non-invertible symmetries, focusing on 1+1d CFTs. We describe a generalized version of Noether’s theorem, where continuous non-invertible symmetries are associated to non-local conser…

When are duality defects group-theoretical? Open

Zhengdi Sun, Yunqin Zheng · 2025

A bstract A quantum field theory with a finite abelian symmetry G may be equipped with a non-invertible duality defect associated with gauging G . For certain G , duality defects admit an alternative construction where one starts with inve…

Intrinsically/purely gapless-SPT from non-invertible duality transformations Open

Linhao Li, Masaki Oshikawa, Yunqin Zheng · 2025

The Kennedy-Tasaki (KT) transformation was used to construct the gapped symmetry protected topological (SPT) phase from the symmetry breaking phase with open boundary condition, and was generalized in our proceeding work [Phys. Rev. B 108,…

Non-invertible and higher-form symmetries in 2+1d lattice gauge theories Open

Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng · 2025

We explore exact generalized symmetries in the standard 2+1d lattice \mathbb{Z}_2 gauge theory coupled to the Ising model, and compare them with their continuum field theory counterparts. One model has a (non-anomalous) non-invertible…

Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra Open

Yichul Choi, Brandon C. Rayhaun, Yunqin Zheng · 2024

We derive a refined version of the Affleck-Ludwig-Cardy formula for a 1+1D conformal field theory, which controls the asymptotic density of high energy states on an interval transforming under a given representation of a noninvertible glob…

Noninvertible Symmetry-Resolved Affleck-Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra Open

Yichul Choi, Brandon C. Rayhaun, Yunqin Zheng · 2024

We derive a refined version of the Affleck-Ludwig-Cardy formula for a 1+1d conformal field theory, which controls the asymptotic density of high energy states on an interval transforming under a given representation of a noninvertible glob…

Generalized Tube Algebras, Symmetry-Resolved Partition Functions, and Twisted Boundary States Open

Yichul Choi, Brandon C. Rayhaun, Yunqin Zheng · 2024

We introduce a class of generalized tube algebras which describe how finite, non-invertible global symmetries of bosonic 1+1d QFTs act on operators which sit at the intersection point of a collection of boundaries and interfaces. We develo…

Decorated defect construction of gapless-SPT states Open

Linhao Li, Masaki Oshikawa, Yunqin Zheng · 2024

Symmetry protected topological (SPT) phases are one of the simplest, yet nontrivial, gapped systems that go beyond the Landau paradigm. In this work, we study an extension of the notion of SPT for gapless systems, namely, gapless symmetry …

Dimensionally reducing generalized symmetries from (3+1)-dimensions Open

Emily Nardoni, Matteo Sacchi, Orr Sela, Gabi Zafrir, Yunqin Zheng · 2024

Non-invertible and higher-form symmetries in 2+1d lattice gauge theories Open

Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng · 2024

We explore exact generalized symmetries in the standard 2+1d lattice $\mathbb{Z}_2$ gauge theory coupled to the Ising model, and compare them with their continuum field theory counterparts. One model has a (non-anomalous) non-invertible sy…

Dimensionally Reducing Generalized Symmetries from (3+1)-Dimensions Open

Emily Nardoni, Matteo Sacchi, Orr Sela, Gabi Zafrir, Yunqin Zheng · 2024

Recently there has been an increasing interest in the study of generalized symmetries in dimensions higher than two. This has lead to the discovery of various manifestations of generalized symmetries, notably higher-group and non-invertibl…

Backfiring Bosonisation Open

Philip Boyle Smith, Yunqin Zheng · 2024

For a fermionic quantum field theory in $d=1+1$ dimensions, there is a subtle difference between summing over spin structures and gauging $(-1)^F$. If the gravitational anomaly vanishes mod 16, then both operations are equivalent and yield…

Classification of chiral fermionic CFTs of central charge $\le$ 16 Open

Philip Boyle Smith, Ying‐Hsuan Lin, Yuji Tachikawa, Yunqin Zheng · 2024

We classify two-dimensional purely chiral unitary conformal field theories which are defined on two-dimensional surfaces equipped with spin structure and have central charge less than or equal to 16 , and discuss their duality webs. This…

Report on scipost_202311_00013v1 Open

Philip Smith, Ying‐Hsuan Lin, Yuji Tachikawa, Yunqin Zheng · 2023

We classify two-dimensional purely chiral unitary conformal field theories which are defined on two-dimensional surfaces equipped with spin structure and have central charge less than or equal to 16, and discuss their duality webs.This res…

Subsystem non-invertible symmetry operators and defects Open

Weiguang Cao, Linhao Li, Masahito Yamazaki, Yunqin Zheng · 2023

We explore non-invertible symmetries in two-dimensional lattice models with subsystem \mathbb Z_2 symmetry. We introduce a subsystem \mathbb Z_2 -gauging procedure, called the subsystem Kramers-Wannier transformation, which general…

Symmetry TFTs and anomalies of non-invertible symmetries Open

Justin Kaidi, Emily Nardoni, Gabi Zafrir, Yunqin Zheng · 2023

A bstract It is known that the ’t Hooft anomalies of invertible global symmetries can be characterized by an invertible TQFT in one higher dimension. The analogous statement remains to be understood for non-invertible symmetries. In this n…

When are Duality Defects Group-Theoretical? Open

Zhengdi Sun, Yunqin Zheng · 2023

A quantum field theory with a finite abelian symmetry $G$ may be equipped with a non-invertible duality defect associated with gauging $G$. For certain $G$, duality defects admit an alternative construction where one starts with invertible…

Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations Open

Linhao Li, Masaki Oshikawa, Yunqin Zheng · 2023

The Kennedy-Tasaki (KT) transformation was used to construct the gapped symmetry protected topological (SPT) phase from the symmetry breaking phase with open boundary condition, and was generalized in our proceeding work [L. Li et al. arXi…

Report on 2303.16917v1 Open

Philip Smith, Ying-Hsuan Lin, Yuji Tachikawa, Yunqin Zheng · 2023

We classify two-dimensional purely chiral conformal field theories which are defined on twodimensional surfaces equipped with spin structure and have central charge less than or equal to 16, and discuss their duality webs.This result can b…

Report on 2304.09886v2 Open

Weiguang Cao, Linhao Li, Masahito Yamazaki, Yunqin Zheng · 2023

We explore non-invertible symmetries in two-dimensional lattice models with subsystem Z 2 symmetry.We introduce a subsystem Z 2 -gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers…

Report on 2304.09886v2 Open

Weiguang Cao, Linhao Li, Masahito Yamazaki, Yunqin Zheng · 2023

We explore non-invertible symmetries in two-dimensional lattice models with subsystem Z 2 symmetry.We introduce a subsystem Z 2 -gauging procedure, called the subsystem Kramers-Wannier transformation, which generalizes the ordinary Kramers…

Report on 2303.16917v1 Open

Philip Smith, Ying‐Hsuan Lin, Yuji Tachikawa, Yunqin Zheng · 2023

We classify two-dimensional purely chiral conformal field theories which are defined on twodimensional surfaces equipped with spin structure and have central charge less than or equal to 16, and discuss their duality webs.This result can b…

Classification of chiral fermionic CFTs of central charge $\le 16$ Open

Philip Boyle Smith, Ying‐Hsuan Lin, Yuji Tachikawa, Yunqin Zheng · 2023

We classify two-dimensional purely chiral conformal field theories which are defined on two-dimensional surfaces equipped with spin structure and have central charge less than or equal to 16, and discuss their duality webs. This result can…

Non-Invertible Duality Transformation Between SPT and SSB Phases Open

Linhao Li, Masaki Oshikawa, Yunqin Zheng · 2023

In 1992, Kennedy and Tasaki constructed a non-local unitary transformation that maps between a $\mathbb{Z}_2\times \mathbb{Z}_2$ spontaneously symmetry breaking phase and the Haldane gap phase, which is a prototypical Symmetry-Protected To…

Symmetry TFTs and Anomalies of Non-Invertible Symmetries Open

Justin Kaidi, Emily Nardoni, Gabi Zafrir, Yunqin Zheng · 2023

It is known that the 't Hooft anomalies of invertible global symmetries can be characterized by an invertible TQFT in one higher dimension. The analogous statement remains to be understood for non-invertible symmetries. In this note we dis…

Symmetry TFTs for Non-Invertible Defects Open

Justin Kaidi, Kantaro Ohmori, Yunqin Zheng · 2022

Given any symmetry acting on a $d$-dimensional quantum field theory, there is an associated $(d+1)$-dimensional topological field theory known as the Symmetry TFT (SymTFT). The SymTFT is useful for decoupling the universal quantities of qu…

Boson-fermion duality with subsystem symmetry Open

Weiguang Cao, Masahito Yamazaki, Yunqin Zheng · 2022

We explore an exact duality in $(2+1)$d between the fermionization of a bosonic theory with a $\mathbb{Z}_2$ subsystem symmetry and a fermionic theory with a $\mathbb{Z}_2$ subsystem fermion parity symmetry. A typical example is the dualit…

Non-invertible symmetries of $$ \mathcal{N} $$ = 4 SYM and twisted compactification Open

Justin Kaidi, Gabi Zafrir, Yunqin Zheng · 2022

Decorated Defect Construction of Gapless-SPT States Open

Linhao Li, Masaki Oshikawa, Yunqin Zheng · 2022

Symmetry protected topological (SPT) phases are one of the simplest, yet nontrivial, gapped systems that go beyond the Landau paradigm. In this work, we study an extension of the notion of SPT for gapless systems, namely, gapless symmetry …

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