Lorentz symmetry fractionalization and dualities in (2+1)d

Hsin, Po-Shen; Shao, Shu-Heng

doi:10.21468/scipostphys.8.2.018

Cited by 38 publications

(53 citation statements)

References 72 publications

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“…For any gauge theory with Z 2, [1] one form symmetry, and in particular the SU(2) Yang-Mills with any theta parameter [14,15], can be enriched by the SO(3, 1) Lorentz symmetry, 2 via fractionalizing the Lorentz symmetry on the Wilson line operators. This phenomena has been previously explored in [23][24][25] and others, and has been recently termed in [26] poetically as Lorentz symmetry fractionalization. Fractionalization of the Lorentz symmetry on a Wilson line requires that the Wilson line transforms projectively under SO(3, 1), i.e., the self statistics is shifted by h = 1/2.…”

Section: New Aspects: Lorentz Symmetry Enrichmentsmentioning

confidence: 96%

“…It is also illuminating to refer twisting the gauge bundle constraint from (2.4) to (2.5) as Lorentz symmetry fractionalization. See [26] for the related discussions on 3d Chern-Simons (matter) theories and [29,30] on 4d U(1) gauge theories.…”

Section: Four Siblings and Anomaliesmentioning

confidence: 99%

“…One needs to find a proper fractionalization of the Lorentz symmetry (whose background is w 2 ) to further match the anomaly πw 2 B. Denote the topological spin of the Z 2, [1] generator s in SU(2) 1 as h(s). The additional anomaly π w 2 B modifies the topological spin of s by [26] h(s) → h(s) + 1 2 mod 1.…”

Section: Domain Wall Formentioning

confidence: 99%

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Gauge enhanced quantum criticality and time reversal deconfined domain wall: SU(2) Yang-Mills dynamics with topological terms

Wang

You

Zheng

2020

Phys. Rev. Research

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We explore the low energy dynamics of the four siblings of Lorentz symmetry enriched SU(2) Yang-Mills theory with a theta term at θ = π in (3 + 1)d. Due to a mixed anomaly between time reversal symmetry and the center symmetry, the low energy dynamics must be nontrivial. We focus on two possible scenarios: 1) time reversal symmetry is spontaneously broken by the two confining vacua, and 2) the low energy theory is described by a U(1) Maxwell gauge theory (e.g. U(1) spin liquid in condensed matter) which is deconfined and gapless while preserving time reversal symmetry. In the first scenario, we first identify the global symmetry on the time reversal domain wall, where time reversal symmetry in the bulk induces a Z 2 unitary symmetry on the domain wall. We discuss how the Lorentz symmetry and the unitary Z 2 symmetry enrich the domain wall theory. In the second scenario, we relate the symmetry enrichments of the SU(2) Yang-Mills to that of the U(1) Maxwell gauge theory. This further opens up the possibility that SU(2) QCD with large and odd flavors of fermions could be a direct second order phase transition between two phases of U(1) gauge theories as well as between a U(1) gauge theory and a trivial vacuum (e.g. a trivial paramagnet), where the gauge group is enhanced to be non

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Section: New Aspects: Lorentz Symmetry Enrichmentsmentioning

confidence: 96%

Section: Four Siblings and Anomaliesmentioning

confidence: 99%

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Gauge enhanced quantum criticality and time reversal deconfined domain wall: SU(2) Yang-Mills dynamics with topological terms

Wang

You

Zheng

2020

Phys. Rev. Research

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“…Writing cup product in the action requires such a ring structure, but here such a choice is made in (3.37) which defines a pairing on H 2 (M, Z(G)). 18 has the bosonic line labelled by (p (…”

Section: Relation Between Continuous and Discrete Theta Termsmentioning

confidence: 99%

Line operators of gauge theories on non-spin manifolds

Ang

Roumpedakis

Seifnashri

2020

J. High Energ. Phys.

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We study four-dimensional gauge theories on oriented and non-spin spacetime manifolds. On such manifolds, each line operator arises only either as a boson or a fermion. Based on physical arguments, a method of systematically assigning spin labels to line operators is proposed, and several consistency checks are performed. This is used to classify all possible sets of allowed line operators -including their spins -for gauge theories with simple Lie algebras. The Lagrangian descriptions of the theories with these sets of allowed line operators are given. Finally, the one-form symmetries of these theories are studied by coupling to background gauge fields, and their 't Hooft anomalies are computed. D Consistency with Wu's Formula E Normalization of theta terms 46F Relation between discrete and continuous theta terms 4712 Fermionic electric lines are only possible when Γe = Z(G) has a Z2 subgroup, which couples to (−1) F ∈ Spin(4) of the Lorentz symmetry.

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“…Physically [16,33,34], different extensions (1.12) correspond to different Lorentz symmetry fractionalizations on the symmetry defects of G e, [1]…”

Section: Gauging G Emergent Symmetries and Anomaliesmentioning

confidence: 99%

Higher anomalies, higher symmetries, and cobordisms III: QCD matter phases anew

Wan

Wang

2020

Nuclear Physics B

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We discuss the topological terms, the global symmetries and their 't Hooft anomalies of pure gauge theories in various dimensions, with dynamical gauge group G, the Lorentz symmetry group G Lorentz , and the internal global symmetry G e,[1] × G m, [d−3] which consists of 1-form electric center symmetry G e,[1] and (d − 3) form magnetic symmetry G m, [d−3] . The topological terms are determined by the cobordism invariants (Ω d ) G ′ where G ′ is the group extension of G Lorentz by G, which also characterize the invertible TQFTs or SPTs with global symmetry G ′ . The 't Hooft anomalies are determined by the cobordism invariants (Ω d+1 ) G ′′ where G ′′ is the symmetry extension of G Lorentz by the higher form symmetry G e,[1] × G m, [d−3] . Different symmetry extensions correspond to different fractionalizations of G Lorentz quantum numbers on the symmetry defects of G e,[1] × G m, [d−3] . We compute the cobordism groups/invariants described above for G = U(1), SU(2) and SO(3) in d ≤ 5, thus systematically classifies all the topological terms and the 't Hooft anomalies of d dimensional quantum gauge theories with the above gauge groups. December 2019W −

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Lorentz symmetry fractionalization and dualities in (2+1)d

Cited by 38 publications

References 72 publications

Gauge enhanced quantum criticality and time reversal deconfined domain wall: SU(2) Yang-Mills dynamics with topological terms

Gauge enhanced quantum criticality and time reversal deconfined domain wall: SU(2) Yang-Mills dynamics with topological terms

Line operators of gauge theories on non-spin manifolds

Higher anomalies, higher symmetries, and cobordisms III: QCD matter phases anew

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