Symmetry TFTs for Non-Invertible Defects

Kaidi, Justin; Ohmori, Kantaro; Zheng, Yunqin

doi:10.48550/arxiv.2209.11062

Cited by 13 publications

(25 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Detailed computations are collected in several appendices. While this work was nearing completion, the paper [55], which deals with a construction similar to ours, appeared on the arXiv.…”

Section: Introductionmentioning

confidence: 82%

The holography of non-invertible self-duality symmetries

Antinucci¹,

Benini²,

Copetti³

et al. 2022

Preprint

View full text Add to dashboard Cite

We study how non-invertible self-duality defects arise in theories with a holographic dual. We focus on the paradigmatic example of su(N ) N = 4 SYM. The theory is known to have non-invertible duality and triality defects at τ = i and τ = e 2πi/3 , respectively. At these points in the gravitational moduli space, the gauged SL(2, Z) duality symmetry of type IIB string theory is spontaneously broken to a finite subgroup G, giving rise to a discrete emergent G gauge field. After reduction on the internal manifold, the low-energy physics is dominated by an interesting 5d Chern-Simons theory, further gauged by G, that we analyze and which gives rise to the self-duality defects in the boundary theory. Using the five-dimensional bulk theory, we compute the fusion rules of those defects in detail. The methods presented here are general and may be used to investigate such symmetries in other theories with a gravity dual.

show abstract

“…Detailed computations are collected in several appendices. While this work was nearing completion, the paper [55], which deals with a construction similar to ours, appeared on the arXiv.…”

Section: Introductionmentioning

confidence: 82%

The holography of non-invertible self-duality symmetries

Antinucci¹,

Benini²,

Copetti³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…This is precisely the mapping between symmetry and twist sectors ( u, t) = (t, u) derived using the Kramers-Wannier transformation on the lattice. The fusion rule of the topological interface between X and X /Z 2 can also be derived, following [42,43,45,48]. We will not repeat the derivation here, and refer the interested readers to these references, e.g.…”

Section: Kramers-wannier Transformation and Z 2 Gaugingmentioning

confidence: 99%

“…We will not repeat the derivation here, and refer the interested readers to these references, e.g. Section 2 of [43]. One remark is that in deriving the fusion rule between the duality interfaces N × N , one does not turn on the Z 2 defects U in the vicinity of the locus of N , hence the fusion rule corresponds to the left panel of Figure 3.…”

Section: Kramers-wannier Transformation and Z 2 Gaugingmentioning

confidence: 99%

“…In particular, the transformations for both spin-1 and two spin- 1 2 systems are non-unitary transformations and satisfy the non-invertible fusion rules, which is a generalization of the famous Kramers-Wannier duality transformation. Such duality transformations have been extensively discussed in recent years, both in (1 + 1)d [33][34][35][36][37][38][39][40][41] and in higher dimensions [42][43][44][45][46][47][48][49][50][51][52]. When the system is invariant under the duality transformation, the operator N KT becomes a non-invertible symmetry of the system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-Invertible Duality Transformation Between SPT and SSB Phases

Li¹,

Oshikawa²,

Zheng³

2023

Preprint

View full text Add to dashboard Cite

In 1992, Kennedy and Tasaki constructed a non-local unitary transformation that maps between a Z 2 × Z 2 spontaneously symmetry breaking phase and the Haldane gap phase, which is a prototypical Symmetry-Protected Topological phase in modern framework, on an open spin chain. In this work, we propose a way to define it on a closed chain, by sacrificing unitarity. The operator realizing such a non-unitary transformation satisfies non-invertible fusion rule, and implements a generalized gauging of the Z 2 × Z 2 global symmetry. These findings connect the Kennedy-Tasaki transformation to numerous other concepts developed for SPT phases, and opens a way to construct SPT phases systematically using the duality mapping.

show abstract

“…The string theoretic realization has to capture some of the salient physical properties of the QFTs, in particular the generalized symmetries and their 't Hooft anomalies, which are robust under RG-flow. The symmetry structure of a QFT can be encoded in the so-called Symmetry Topological Field Theory (SymTFT or Symmetry TFT) [76][77][78], see [28,29,31,[79][80][81] for recent applications.…”

Section: Jhep02(2023)226 1 Introductionmentioning

confidence: 99%

Symmetry TFTs for 3d QFTs from M-theory

Beest

Gould

Schäfer‐Nameki

et al. 2023

J. High Energ. Phys.

View full text Add to dashboard Cite

We derive the Symmetry Topological Field Theories (SymTFTs) for 3d supersymmetric quantum field theories (QFTs) constructed in M-theory either via geometric engineering or holography. These 4d SymTFTs encode the symmetry structures of the 3d QFTs, for instance the generalized global symmetries and their ’t Hooft anomalies. Using differential cohomology, we derive the SymTFT by reducing M-theory on a 7-manifold Y7, which either is the link of a conical Calabi-Yau four-fold or part of an AdS4× Y7 holographic solution. In the holographic setting we first consider the 3d $$ \mathcal{N} $$ N = 6 ABJ(M) theories and derive the BF-couplings, which allow the identification of the global form of the gauge group, as well as 1-form symmetry anomalies. Secondly, we compute the SymTFT for 3d $$ \mathcal{N} $$ N = 2 quiver gauge theories whose holographic duals are based on Sasaki-Einstein 7-manifolds of type Y7 = Yp,k($$ \mathbbm{CP} $$ CP 2). The SymTFT encodes 0- and 1-form symmetries, as well as potential ’t Hooft anomalies between these. Furthermore, by studying the gapped boundary conditions of the SymTFT we constrain the allowed choices for U(1) Chern-Simons terms in the dual field theory.

show abstract

Symmetry TFTs for Non-Invertible Defects

Cited by 13 publications

References 54 publications

The holography of non-invertible self-duality symmetries

The holography of non-invertible self-duality symmetries

Non-Invertible Duality Transformation Between SPT and SSB Phases

Symmetry TFTs for 3d QFTs from M-theory

Contact Info

Product

Resources

About