Gauge theory generalization of the fermion doubling theorem

Kravec, Shauna; McGreevy, John

doi:10.1103/physrevlett.111.161603

Cited by 32 publications

(59 citation statements)

References 61 publications

(106 reference statements)

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“…It is apparent that the discrete symmetries (3.9) and (3.10) play a striking role, since they select the edge dynamics: 4D boundary actions are possible only if one of the two TR symmetries are requested in the bulk. In this sense the edge states are "protected" by the discrete symmetries, as remarked in [22]. Moreover, and quite remarkably, the action (5.35) displays a true electromagnetic duality, which exchanges the "electric" and "magnetic" fields, together with the inversion of the coupling constant.…”

Section: Jhep04(2014)142mentioning

confidence: 77%

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Holography in flat spacetime: 4D theories and electromagnetic duality on the border

Amoretti

Braggio

Caruso

et al. 2014

J. High Energ. Phys.

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We consider a free topological model in 5D Euclidean flat spacetime, built from two rank-2 tensor fields. Despite the fact that the bulk of the model does not have any particular physical interpretation, on its 4D planar edge nontrivial gauge field theories are recovered, whose features descend from the gauge and discrete symmetries of the bulk. In particular the 4D dynamics cannot be obtained without imposing a Time Reversal invariance in the bulk. Remarkably, one of the two possible edge models selected by the Time Reversal symmetries displays a true electromagnetic duality, which relates strong and weak coupling regimes. Moreover the same model, when considered on-shell, coincides with the Maxwell theory, which therefore can be thought of as a 4D boundary theory of a seemingly harmless 5D topological model.

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Section: Jhep04(2014)142mentioning

confidence: 77%

“…only if one of the two Time Reversal discrete symmetries (3.9) or (3.10) are respected. In this sense, the edge states of the model (6.1) are "protected", as guessed in [22].…”

Section: Summary and Discussionmentioning

confidence: 88%

Holography in flat spacetime: 4D theories and electromagnetic duality on the border

Amoretti

Braggio

Caruso

et al. 2014

J. High Energ. Phys.

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“…Thus our discussion will be purely in the Chern-Simons formulation. We begin by noting that this theory has been extensively studied for a variety of purposes [30,[32][33][34]. A careful quantum treatment has been performed in [35].…”

Section: Discrete 1-form Global Symmetries and Holographymentioning

confidence: 99%

“…We now finally need the exact solution to the wave equation (30). The solution that is regular as r → 0 is a particular Bessel function:…”

Section: Vacuum Correlations and Marginal Deformationsmentioning

confidence: 99%

Generalized global symmetries and holography

2018

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We study the holographic duals of four-dimensional field theories with 1-form global symmetries, both discrete and continuous. Such higher-form global symmetries are associated with antisymmetric tensor gauge fields in the bulk. Various different realizations are possible: we demonstrate that a Maxwell action for the bulk antisymmetric gauge field results in a non-conformal field theory with a marginally running double-trace coupling. We explore its hydrodynamic behavior at finite temperature and make contact with recent symmetry-based formulations of magnetohydrodynamics. We also argue that discrete global symmetries on the boundary are dual to discrete gauge theories in the bulk. Such gauge theories have a bulk Chern-Simons description: we clarify the conventional 0-form case and work out the 1-form case. Depending on boundary conditions, such discrete symmetries may be embedded in continuous higher-form symmetries that are spontaneously broken. We study the resulting boundary Goldstone mode, which in the 1-form case may be thought of as a boundary photon. Our results clarify how the global form of the field theory gauge group is encoded in holography. Finally, we study the interplay of Maxwell and Chern-Simons terms put together. We work out the operator content and demonstrate the existence of new backreacted anisotropic scaling solutions that carry higher-form charge.

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“…One may wonder whether it is possible to change an electric charge into a magnetic monopole, but Ref. [66] pointed out this is impossible in a strictly 3D system. Below we will discuss these two types of Z 2 actions in turn.…”

Section: U(1) Quantum Spin Liquids Enriched By Z 2 × T Symmetrymentioning

confidence: 99%

Symmetry enriched U(1) quantum spin liquids

2018

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We classify and characterize three-dimensional U(1) quantum spin liquids [deconfined U(1) gauge theories] with global symmetries. These spin liquids have an emergent gapless photon and emergent electric/magnetic excitations (which we assume are gapped). We first discuss in great detail the case with time-reversal and SO(3) spin rotational symmetries. We find there are 15 distinct such quantum spin liquids based on the properties of bulk excitations. We show how to interpret them as gauged symmetry-protected topological states (SPTs). Some of these states possess fractional response to an external SO(3) gauge field, due to which we dub them "fractional topological paramagnets." We identify 11 other anomalous states that can be grouped into three anomaly classes. The classification is further refined by weakly coupling these quantum spin liquids to bosonic symmetry protected topological (SPT) phases with the same symmetry. This refinement does not modify the bulk excitation structure but modifies universal surface properties. Taking this refinement into account, we find there are 168 distinct such U(1) quantum spin liquids. After this warm-up, we provide a general framework to classify symmetry enriched U(1) quantum spin liquids for a large class of symmetries. As a more complex example, we discuss U(1) quantum spin liquids with time-reversal and Z 2 symmetries in detail. Based on the properties of the bulk excitations, we find there are 38 distinct such spin liquids that are anomaly-free. There are also 37 anomalous U(1) quantum spin liquids with this symmetry. Finally, we briefly discuss the classification of U(1) quantum spin liquids enriched by some other symmetries.

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Gauge theory generalization of the fermion doubling theorem

Cited by 32 publications

References 61 publications

Holography in flat spacetime: 4D theories and electromagnetic duality on the border

Holography in flat spacetime: 4D theories and electromagnetic duality on the border

Generalized global symmetries and holography

Symmetry enriched U(1) quantum spin liquids

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