Volume-preserving diffeomorphism as nonabelian higher-rank gauge  symmetry

Du, Yi-Hsien; Mehta, Umang; Nguyen, Dung Xuan; Son, D.

doi:10.21468/scipostphys.12.2.050

Cited by 24 publications

(28 citation statements)

References 54 publications

(117 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, the consequences of global symmetry are oftentimes conveniently expressed in terms of invariance of the generating functional of the theory under gauge transformations of a set of background fields. The background gauge invariance corresponding to the class of dipole-type symmetries considered here is worked out in Appendix D. This provides a natural link between the present paper and the recent work of Du et al [12] on invariance of systems with fracton-like mobility constraints under volume-preserving diffeomorphisms.…”

Section: Introductionmentioning

confidence: 63%

See 1 more Smart Citation

Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

Brauner¹,

Yamamoto²,

Yokokura³

2023

Preprint

View full text Add to dashboard Cite

We demonstrate the general existence of a local dipole conservation law in bosonic field theory. The scalar charge density arises from the symplectic form of the system, whereas the tensor current descends from its stress tensor. The algebra of spatial translations becomes centrally extended in presence of field configurations with a finite nonzero charge. Furthermore, when the symplectic form is closed but not exact, the system may, surprisingly, lack a well-defined momentum density. This leads to a theorem for the presence of additional light modes in the system whenever the short-distance physics is governed by a translationally invariant local field theory. We also illustrate this mechanism for axion electrodynamics as an example of a system with Nambu-Goldstone modes of higher-form symmetries.

show abstract

Section: Introductionmentioning

confidence: 63%

“…The current J µ , and hence the integral charge Q, is conserved off-shell. If we now on top of that impose the equation of motion, we get the on-shell relation (12). This guarantees via (1) the conservation of D i and X as defined by ( 2) and (3).…”

Section: Dipole Conservation Laws From Translation Invariancementioning

confidence: 98%

Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

Brauner¹,

Yamamoto²,

Yokokura³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Thus, a U (1) charge, whose worldline is given by C, is fractonic. One can check that Q(S) indeed generates a U (1) phase rotation of W q (C), 12 e iαQ(S) W q (C) = e iαqL(S,C) W q (C), (75…”

Section: Ementioning

confidence: 99%

“…Fractons are excitations with mobility restrictions, and phases with fractons constitute a new class of quantum phases of matter [1,2]. Gapless fractonic phases have been described by higher-rank gauge theories [3][4][5][6][7][8][9][10][11][12][13], including the scalar/vector charge gauge theories. Higher-rank gauge fields appear as a result of a gauging of the multipole algebra [14][15][16] (see also discussions on the relation between multipoles and fracton phases in Refs.…”

Section: Introductionmentioning

confidence: 99%

A symmetry principle for gauge theories with fractons

Hirono¹,

You²,

Angus³

et al. 2022

Preprint

View full text Add to dashboard Cite

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

show abstract

“…Our methods naturally extend to field theories with conserved multipole moments, including those with conserved dipole moment and quadrupole trace. This particular symmetry pattern is perhaps the most experimentally relevant one on the market, given the arguments that these symmetries approximately govern real-world systems including vortices in superfluid helium [14,15], defects in 2 + 1-dimensional elastic media [16], and the lowest Landau level of a quantum Hall state [17].…”

Section: Introductionmentioning

confidence: 99%

Fractons in curved space

Jain,

Jensen

2021

Preprint

View full text Add to dashboard Cite

We consistently couple simple continuum field theories with fracton excitations to curved spacetime backgrounds. We consider homogeneous and isotropic fracton field theories, with a conserved U (1) charge and dipole moment. Coupling to background fields allows us to consistently define a stress-energy tensor for these theories and obtain the respective Ward identities. Along the way, we find evidence for a mixed gauge-gravitational anomaly in the symmetric tensor gauge theory which naturally couples to conserved dipoles. Our results generalise to systems with arbitrarily higher conserved moments, in particular, a conserved quadrupole moment.

show abstract

Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

Cited by 24 publications

References 54 publications

Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

A symmetry principle for gauge theories with fractons

Fractons in curved space

Contact Info

Product

Resources

About