Lifshitz symmetry: Lie algebras, spacetimes and particles

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

doi:10.48550/arxiv.2206.11806

Cited by 3 publications

(3 citation statements)

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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.…”

Section: Summary and Discussionmentioning

confidence: 99%

A symmetry principle for gauge theories with fractons

Hirono¹,

You²,

Angus³

et al. 2022

Preprint

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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 1form 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. CONTENTSI. Introduction II. Fractons from nonuniform higher-form symmetries A. Nonuniform higher-form symmetries B. Strategy to realize fractons C. Deformation of symmetry generators III. Gauge theory with U (1) and dipole symmetries A. U (1) and dipole symmetries and their gauging B. Gauge theory of U (1) charge-and dipole-gauge fields C. Low energy limit and the relation to the scalar charge gauge theory D. Number of gapless modes E. Higher-form symmetries and fractons F. Dual theory G. SSB of higher-form symmetries H. Extended operators at low energies I. Gauging of nonuniform higher-form symmetries, 't Hooft anomalies, and an SPT action J. Higgsing and fracton order K. Variants of the scalar charge gauge theory IV. Vector charge gauge theory from nonuniform symmetries

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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.…”

Section: Summary and Discussionmentioning

confidence: 99%

A symmetry principle for gauge theories with fractons

Hirono¹,

You²,

Angus³

et al. 2022

Preprint

View full text Add to dashboard Cite

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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., [62]). The extension of sim(d) is the original Lifshitz algebra, where the parameter α is typically denoted z:…”

Section: Aristotelian Lie Algebrasmentioning

confidence: 99%

A non-lorentzian primer

Bergshoeff¹,

Figueroa-O’Farrill²,

Gomis³

2022

Preprint

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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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“…Before describing them, it is perhaps useful to say something about where they come from. They arose initially in a forthcoming follow-up paper to [13] in which we discuss geometries associated to Lie algebras obtained from Lifshitz Lie algebras by the addition of boosts. The homogeneous pp-wave spacetimes in question are geometric realisations of effective Klein pairs (g, h) where g is a deformation of the centrally extended static kinematical Lie algebra and h is spanned by what could be interpreted as spatial rotations and boosts.…”

Section: K -mentioning

confidence: 99%