On Higher-Form Fracton Hydrodynamics with Momentum Conservation
Abstract
Momentum conservation is common in fluids, yet it may be incompatible with the hydrodynamics of theories with exotic conservation laws (such as fracton hydrodynamics) unless symmetries are spontaneously broken. Using the Martin-Siggia-Rose (MSR) effective field theory formalism, we develop a representation-theoretic framework for the hydrodynamics of translationally invariant systems with exotic conservation laws without spontaneous symmetry breaking. Under mild assumptions on the form of hydrodynamics, we show that such theories must satisfy two representation theoretic consistency conditions and a generalized Gauss's law constraint. Higher-form symmetries satisfy these conditions and we derive their ideal hydrodynamics; in three dimensions, the one-form case produces ideal non-relativistic magnetohydrodynamics. Finally, we prove that no other theories are compatible with momentum conservation in SO(3) nor SO(d), for sufficiently large odd d.
Related
- A Universal Approach to Hydrodynamics in Higher Dimensions via Tensor Networks
- Stationarity and angular momentum conservation in pulsar spin noise
- Angular momentum conservation in two-atom superradiance
- Momentum conservation for ab initio calculations with pseudopotentials via a phase space electronic structure formulation
- Zero of the proton electric form factor in the finite value of the spacelike momentum transfer squared
BibTeX
@misc{bobell2026higherform,
title = {{On Higher-Form Fracton Hydrodynamics with Momentum Conservation}},
author = {Ben Bobell and Rahul Nandkishore and Andrew Lucas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26862},
eprint = {2610.26862},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26862},
}
RIS
TY - UNPB
TI - On Higher-Form Fracton Hydrodynamics with Momentum Conservation
AU - Ben Bobell
AU - Rahul Nandkishore
AU - Andrew Lucas
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26862
UR - https://arxiv.org/abs/2610.26862
AB - Momentum conservation is common in fluids, yet it may be incompatible with the hydrodynamics of theories with exotic conservation laws (such as fracton hydrodynamics) unless symmetries are spontaneously broken. Using the Martin-Siggia-Rose (MSR) effective field theory formalism, we develop a representation-theoretic framework for the hydrodynamics of translationally invariant systems with exotic conservation laws without spontaneous symmetry breaking. Under mild assumptions on the form of hydrodynamics, we show that such theories must satisfy two representation theoretic consistency conditions and a generalized Gauss's law constraint. Higher-form symmetries satisfy these conditions and we derive their ideal hydrodynamics; in three dimensions, the one-form case produces ideal non-relativistic magnetohydrodynamics. Finally, we prove that no other theories are compatible with momentum conservation in SO(3) nor SO(d), for sufficiently large odd d.
ER -