Lifshitz symmetry: Lie algebras, spacetimes and particles

Figueroa-O’Farrill, José; Grassie, Ross; Prohazka, Stefan

doi:10.21468/scipostphys.14.3.035

Cited by 8 publications

(4 citation statements)

References 53 publications

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“…The tools used in this work are not restricted to the Carroll and dipole groups and we will discuss other particles with restricted mobility in a future work [86].…”

Section: Jhep10(2023)041mentioning

confidence: 99%

Quantum Carroll/fracton particles

Figueroa-O’Farrill,

Pérez,

Prohazka

2023

J. High Energ. Phys.

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We classify and relate unitary irreducible representations (UIRs) of the Carroll and dipole groups, i.e., we define elementary quantum Carroll and fracton particles and establish a correspondence between them. Whenever possible, we express the UIRs in terms of fields on Carroll/Aristotle spacetime subject to their free field equations.We emphasise that free massive (or “electric”) Carroll and fracton quantum field theories are ultralocal field theories and highlight their peculiar and puzzling thermodynamic features. We also comment on subtle differences between massless and “magnetic” Carroll field theories and discuss the importance of Carroll and fractons symmetries for flat space holography.

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“…The tools used in this work are not restricted to the Carroll and dipole groups and we will discuss other particles with restricted mobility in a future work [86].…”

Section: Jhep10(2023)041mentioning

confidence: 99%

Quantum Carroll/fracton particles

Figueroa-O’Farrill,

Pérez,

Prohazka

2023

J. High Energ. Phys.

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“…• It would be interesting to explore how the current formulation is related to other geometric constructions [64][65][66] as well as the associated interplay with gravitational physics. where Z i j is symmetric, Z i j = Z ji , and Y abi j is symmetric with respect to a ↔ b and i ↔ j, and also Y a bi j = Y i ja b .…”

Section: Summary and Discussionmentioning

confidence: 99%

A symmetry principle for gauge theories with fractons

Hirono,

You,

Angus

et al. 2024

SciPost Phys.

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Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1-form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu-Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the ’t Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.

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“…Changing notation: (H, Z) → (D, H), the Lie algebras in Table 4 are examples of Lifshitz Lie algebras (see, e.g., [69]). The extension of sim(d) is the original Lifshitz algebra, where the parameter α is typically denoted z: In this section we discuss non-lorentzian geometries.…”

Section: Central Extensionsmentioning

confidence: 99%

A non-lorentzian primer

Bergshoeff

Figueroa-O’Farrill

Gomis

2023

SciPost Phys. Lect. Notes

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We review both the kinematics and dynamics of non-lorentzian theories and their associated geometries. First, we introduce non-lorentzian kinematical spacetimes and their symmetry algebras. Next, we construct actions describing the particle dynamics in some of these kinematical spaces using the method of nonlinear realisations. We explain the relation with the coadjoint orbit method. We continue discussing three types of non-lorentzian gravity theories: Galilei gravity, Newton-Cartan gravity and Carroll gravity. Introducing matter, we discuss electric and magnetic non-lorentzian field theories for three different spins: spin-0, spin-1/2 and spin-1, as limits of relativistic theories.

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Lifshitz symmetry: Lie algebras, spacetimes and particles

Cited by 8 publications

References 53 publications

Quantum Carroll/fracton particles

Quantum Carroll/fracton particles

A symmetry principle for gauge theories with fractons

A non-lorentzian primer

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