The authors introduce fractonic solids via a new symmetry that ties fracton mobility to a material, enabling gauge-invariant momentum, boost compatibility, and gravitational coupling.
An Invitation to Higher Gauge Theory
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra that governs 11-dimensional supergravity.
verdicts
UNVERDICTED 5representative citing papers
The five-dimensional topological axion electrodynamics is shown to possess a 3-crossed module structure through modified Stueckelberg couplings required for background gauge invariance.
Formulates 2-connections and gauge transformations for principal 2-bundles using an operational framework based on crossed modules and derived Lie groups.
Field theories with ℤ_N p-form symmetry generically admit a Coulomb phase where the infrared theory is Abelian p-form electrodynamics, illustrated via continuum and lattice examples.
The paper introduces a matrix toy model that inherits p-form gauge symmetry from the functional space of p-brane configurations via symmetric trace after replacing the infinite-dimensional space with finite matrices.
citing papers explorer
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Fractonic solids
The authors introduce fractonic solids via a new symmetry that ties fracton mobility to a material, enabling gauge-invariant momentum, boost compatibility, and gravitational coupling.
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3-Crossed Module Structure in the Five-Dimensional Topological Axion Electrodynamics
The five-dimensional topological axion electrodynamics is shown to possess a 3-crossed module structure through modified Stueckelberg couplings required for background gauge invariance.
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Operational total space theory of principal 2-bundles II: 2-connections and 1- and 2--gauge transformations
Formulates 2-connections and gauge transformations for principal 2-bundles using an operational framework based on crossed modules and derived Lie groups.
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Discrete $p$-Form Symmetry and Higher Coulomb Phases
Field theories with ℤ_N p-form symmetry generically admit a Coulomb phase where the infrared theory is Abelian p-form electrodynamics, illustrated via continuum and lattice examples.
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A toy model for $p$-form gauge symmetry
The paper introduces a matrix toy model that inherits p-form gauge symmetry from the functional space of p-brane configurations via symmetric trace after replacing the infinite-dimensional space with finite matrices.