@article{ISI:000511444200001,
 abstract = {Fractons emerge as charges with reduced mobility in a class of gauge
theories. Here, we generalize fractonic theories of U(1) type to what we
call (k, n)-fractonic Maxwell theory, which employs symmetric rank-n
tensors of k forms (rank-k antisymmetric tensors) as ``vector
potentials.″ The generalization, valid in any spatial dimension d,
has two key manifestations. First, the objects with mobility
restrictions extend beyond simple charges to higher-order multipoles
(dipoles, quadrupoles, etc.) all the way to (n - 1)th-order multipoles,
which we call the order-n fracton condition. Second, these fractonic
charges themselves are characterized by tensorial densities of (k -
1)-dimensional extended objects. For any (k, n), the theory can be
constructed to have a gapless ``photon modes″ with dispersion omega
similar to vertical bar q vertical bar(z), where the integer z can range
from 1 to n.},
 article-number = {085106},
 author = {Shenoy, Vijay B. and Moessner, Roderich},
 doi = {10.1103/PhysRevB.101.085106},
 eissn = {2469-9969},
 issn = {2469-9950},
 journal = {PHYSICAL REVIEW B},
 month = {FEB 6},
 number = {8},
 times-cited = {0},
 title = {(k, n)-fractonic Maxwell theory},
 unique-id = {ISI:000511444200001},
 volume = {101},
 year = {2020}
}