Interacting fractons in 2+1-dimensional quantum field theory

Distler, Jacques; Jafry, Murtaza; Karch, Andreas; Raz, Amir

doi:10.1007/jhep03(2022)070

Cited by 9 publications

(9 citation statements)

References 19 publications

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“…The action is additionally invariant under a symmetry of the form (4. 19), where now Γ (2|1) transforms as well 39) We now see one of the benefits of the first-order formulation, it decouples the symmetry whose Noether current is the gauge non-invariant (4.18), from the symmetry whose current is the Riemann tensor. 26 We now want to gauge the symmetry (4.39).…”

Section: Gauging Higher-biform Symmetriesmentioning

confidence: 95%

“…Since κ multiplies d − 2 in (3.39), we can no longer choose it to make the trace of J µ|ν vanish. 19 In this case, the currents satisfy the equations tr J = a C (2) ,…”

Section: Coupling To Background Gauge Fieldsmentioning

confidence: 99%

“…In particular, in four dimensions, we need traceful contact terms to be able to write the full two-point function. The d = 4 case is written explicitly in equation (D. 19) in appendix D.2.1. As before, we see that this correlator has a 1/p 2 pole, indicating the presence of a massless spin-2 field in the spectrum.…”

Section: Generic Dimension D >mentioning

confidence: 99%

“…Looking at (B. 19)-(B.21), it is clear that in two dimensions, we have a three-way anomaly, where we can choose the current J µν to be one of traceless (β = 0), conserved (β = 1) or dual conserved (β = −1).…”

Section: Conserved Currentmentioning

confidence: 99%

“…There has been a substantial amount of recent work related to the physics of fractons and their relation to these general ideas. More details can be found for example in[17][18][19][20][21][22][23][24] and references therein.…”

mentioning

confidence: 99%

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Gravity as a gapless phase and biform symmetries

Hinterbichler¹,

Hofman²,

Joyce³

et al. 2022

Preprint

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We study effective field theories (EFTs) enjoying (maximal) biform symmetries. These are defined by the presence of a conserved (electric) current that has the symmetries of a Young tableau with two columns of equal length. When these theories also have a topological (magnetic) biform current, its conservation law is anomalous. We go on to show that this mixed anomaly uniquely fixes the two-point function between the electric and magnetic currents. We then perform a Källén-Lehmann spectral decomposition of the current-current correlator, proving that there is a massless mode in the spectrum, whose masslessness is protected by the anomaly. Furthermore, the anomaly gives rise to a universal form of the EFT whose most relevant term-which resembles the linear Einstein action-dominates the infrared physics. As applications of this general formalism, we study the theories of a Galileon superfluid and linearized gravity. Thus, one can view the masslessness of the graviton as being protected by the anomalous biform symmetries. The associated EFT provides an organizing principle for gravity at low energies in terms of physical symmetries, and allows interactions consistent with linearized diffeomorphism invariance. These theories are not ultraviolet-complete-the relevant symmetries can be viewed as emergent-nor do they include the nonlinearities necessary to make them fully diffeomorphism invariant, so there is no contradiction with the expectation that quantum gravity cannot have any global symmetries.

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Section: Gauging Higher-biform Symmetriesmentioning

confidence: 95%

“…Since κ multiplies d − 2 in (3.39), we can no longer choose it to make the trace of J µ|ν vanish. 19 In this case, the currents satisfy the equations tr J = a C (2) ,…”

Section: Coupling To Background Gauge Fieldsmentioning

confidence: 99%

Section: Generic Dimension D >mentioning

confidence: 99%

Section: Conserved Currentmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Gravity as a gapless phase and biform symmetries

Hinterbichler¹,

Hofman²,

Joyce³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

Gravity as a gapless phase and biform symmetries

Hinterbichler

Hofman

Joyce

et al. 2023

J. High Energ. Phys.

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We study effective field theories (EFTs) enjoying (maximal) biform symmetries. These are defined by the presence of a conserved (electric) current that has the symmetries of a Young tableau with two columns of equal length. When these theories also have a topological (magnetic) biform current, its conservation law is anomalous. We go on to show that this mixed anomaly uniquely fixes the two-point function between the electric and magnetic currents. We then perform a Källén-Lehmann spectral decomposition of the current-current correlator, proving that there is a massless mode in the spectrum, whose masslessness is protected by the anomaly. Furthermore, the anomaly gives rise to a universal form of the EFT whose most relevant term — which resembles the linear Einstein action — dominates the infrared physics. As applications of this general formalism, we study the theories of a Galileon superfluid and linearized gravity. Thus, one can view the masslessness of the graviton as being protected by the anomalous biform symmetries. The associated EFT provides an organizing principle for gravity at low energies in terms of physical symmetries, and allows interactions consistent with linearized diffeomorphism invariance. These theories are not ultraviolet-complete — the relevant symmetries can be viewed as emergent — nor do they include the nonlinearities necessary to make them fully diffeomorphism invariant, so there is no contradiction with the expectation that quantum gravity cannot have any global symmetries.

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Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d + 1 dimensions

Honda

Nakanishi

2023

J. High Energ. Phys.

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We study various non-relativistic field theories with exotic symmetries called subsystem symmetries, which have recently attracted much attention in the context of fractons. We start with a scalar theory called ϕ-theory in d + 1 dimensions and discuss its properties studied in literature for d ≤ 3 such as self-duality, vacuum structure, ’t Hooft anomaly, anomaly inflow and lattice regularization. Next we study a theory called chiral ϕ-theory which is an analogue of a chiral boson with subsystem symmetries. Then we discuss theories including fermions with subsystem symmetries. We first construct a supersymmetric version of the ϕ-theory and dropping its bosonic part leads us to a purely fermionic theory with subsystem symmetries called ψ-theory. We argue that lattice regularization of the ψ-theory generically suffers from an analogue of doubling problem as previously pointed out in the d = 3 case. We propose an analogue of Wilson fermion to avoid the “doubling” problem. We also supersymmetrize the chiral ϕ-theory and dropping the bosonic part again gives us a purely fermionic theory. We finally discuss vacuum structures of the theories with fermions and find that they are infinitely degenerate because of spontaneous breaking of subsystem symmetries.

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Interacting fractons in 2+1-dimensional quantum field theory

Cited by 9 publications

References 19 publications

Gravity as a gapless phase and biform symmetries

Gravity as a gapless phase and biform symmetries

Gravity as a gapless phase and biform symmetries

Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d + 1 dimensions

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