Higher Symmetry and Gapped Phases of Gauge Theories

Kapustin, Anton; Thorngren, Ryan

doi:10.1007/978-3-319-59939-7_5

Cited by 167 publications

(328 citation statements)

References 32 publications

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“…We take e to be a boson; there are also Z g 2 gauge theories with fermionic quasiparticles carrying the gauge charge [13,28,[30][31][32]], but we do not consider these theories here. The e quasiparticle feels m as a π flux, so that a statistical phase of π is acquired when e winds around a m quasistring.…”

Section: Symmetry Fractionalization In 3dmentioning

confidence: 99%

“…It was realized that some of the SF patterns are anomalous, i.e., they cannot be realized in strictly 2D systems [14][15][16][17][18][19][20][21][22][23][24][25][26]. Various anomaly detection methods have been proposed to identify such SF patterns.…”

Section: Introductionmentioning

confidence: 99%

“…Various anomaly detection methods have been proposed to identify such SF patterns. The central idea of most methods is based on introducing symmetry fluxes into the system and trying to gauge the global symmetry [10,[22][23][24][25][26]. If the SF pattern can be realized in a strictly 2D model, then the global symmetry can be consistently gauged, resulting in a larger topological theory including the original quasiparticles and the symmetry fluxes and charges.…”

Section: Introductionmentioning

confidence: 99%

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Symmetry fractionalization and anomaly detection in three-dimensional topological phases

Xie

Hermele

2016

Phys. Rev. B

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In a phase with fractional excitations, topological properties are enriched in the presence of global symmetry. In particular, fractional excitations can transform under symmetry in a fractionalized manner, resulting in different symmetry enriched topological (SET) phases. While a good deal is now understood in 2D regarding what symmetry fractionalization patterns are possible, the situation in 3D is much more open. A new feature in 3D is the existence of loop excitations, so to study 3D SET phases, first we need to understand how to properly describe the fractionalized action of symmetry on loops. Using a dimensional reduction procedure, we show that these loop excitations exist as the boundary between two 2D SET phases, and the symmetry action is characterized by the corresponding difference in SET orders. Moreover, similar to the 2D case, we find that some seemingly possible symmetry fractionalization patterns are actually anomalous and cannot be realized strictly in 3D. We detect such anomalies using the flux fusion method we introduced previously in 2D. To illustrate these ideas, we use the 3D Z 2 gauge theory with Z 2 global symmetry as an example, and enumerate and describe the corresponding SET phases. In particular, we find four nonanomalous SET phases and one anomalous SET phase, which we show can be realized as the surface of a 4D system with symmetry protected topological order.

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Section: Symmetry Fractionalization In 3dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Symmetry fractionalization and anomaly detection in three-dimensional topological phases

Xie

Hermele

2016

Phys. Rev. B

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“…These newly introduced action terms are topological since their expressions are wedge products of differential forms. Recently a lot of progress has been made based on these topological terms in gauge theories as well as SPT phases [13,23,[79][80][81]. The presence of interlayer topological interactions leads to twisted G g gauge theories.…”

Section: Gauge Theories Topological Interactions and Global Symmentioning

confidence: 99%

“…Physically, these 3D SETs can be viewed as 3D gapped QSLs that are enriched by unbroken on-site symmetry G s . Given a gauge group G g , there are usually many topologically distinct gauge theories (denoted by GT) including one untwisted and several twisted ones [23,73], as shown in Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Symmetry enrichment in three-dimensional topological phases

Ning

Liu

2016

Phys. Rev. B

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While two-dimensional symmetry-enriched topological phases (SETs) have been studied intensively and systematically, three-dimensional ones are still open issues. We propose an algorithmic approach of imposing global symmetry Gs on gauge theories (denoted by GT) with gauge group Gg. The resulting symmetric gauge theories are dubbed "symmetry-enriched gauge theories" (SEG), which may be served as low-energy effective theories of three-dimensional symmetric topological quantum spin liquids. We focus on SEGs with gauge group Gg = ZN 1 × ZN 2 × · · · and on-site unitary symmetry group Gs = ZK 1 × ZK 2 × · · · or Gs = U(1) × ZK 1 × · · · . Each SEG(Gg, Gs) is described in the path integral formalism associated with certain symmetry assignment. From the path-integral expression, we propose how to physically diagnose the ground state properties (i.e., SET orders) of SEGs in experiments of charge-loop braidings (patterns of symmetry fractionalization) and the mixed multi-loop braidings among deconfined loop excitations and confined symmetry fluxes. From these symmetry-enriched properties, one can obtain the map from SEGs to SETs. By giving full dynamics to background gauge fields, SEGs may be eventually promoted to a set of new gauge theories (denoted by GT * ). Based on their gauge groups, GT * s may be further regrouped into different classes each of which is labeled by a gauge group G * g . Finally, a web of gauge theories involving GT, SEG, SET and GT * is achieved. We demonstrate the above symmetry-enrichment physics and the web of gauge theories through many concrete examples.

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Higher Flavor Symmetries in the Standard Model

Córdova

Koren

2023

Annalen der Physik

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A study of the generalized global flavor symmetries of the Standard Model is initiated. The presence of nonzero triangle diagrams between the U(3)5 flavor currents and the hypercharge current intertwines them in the form of a higher‐group which mixes the zero‐form flavor symmetries with the one‐form magnetic hypercharge symmetry. This higher symmetry structure greatly restricts the possible flavor symmetries that may remain unbroken in any ultraviolet completion that includes magnetic monopoles. In the context of unification, this implies tight constraints on the combinations of fermion species which may be joined into multiplets. Three of four elementary possibilities are reflected in the classic unification models of Georgi–Glashow, , and Pati–Salam. The final pattern is realized non‐trivially in trinification, which exhibits the sense in which Standard Model Yukawa couplings which violate these flavor symmetries may be thought of as spurions of the higher‐group. Such modifications of the ultraviolet flavor symmetries are possible only if new vector‐like matter is introduced with masses suppressed from the unification scale by the Yukawa couplings.

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Higher Symmetry and Gapped Phases of Gauge Theories

Cited by 167 publications

References 32 publications

Symmetry fractionalization and anomaly detection in three-dimensional topological phases

Symmetry fractionalization and anomaly detection in three-dimensional topological phases

Symmetry enrichment in three-dimensional topological phases

Higher Flavor Symmetries in the Standard Model

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