Fractons on curved spacetime in 2 + 1 dimensions

• DOI: 10.21468/scipostphys.18.1.022
• Publication Date: 2025-01-17T11:52:29Z
• Authors: Jelle Hartong; Giandomenico Palumbo; Simon Pekar; Alfredo Perez; Stefan Prohazka
• Keywords: High Energy Physics - Theory; 103028 Relativitätstheorie; Condensed Matter - Strongly Correlated Electrons; High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); Physics; QC1-999; FOS: Physical sciences; 103012 High energy physics; General Relativity and Quantum Cosmology (gr-qc); 103012 Hochenergiephysik; General Relativity and Quantum Cosmology; 103028 Theory of relativity

We study dipole Chern–Simons theory with and without a cosmological constant in 2+12+1 dimensions. We write the theory in a second order formulation and show that this leads to a fracton gauge theory coupled to Aristotelian geometry which can also be coupled to matter. This coupling exhibits the remarkable property of generalizing dipole gauge invariance to curved spacetimes, without placing any limitations on the possible geometries. We also use the second order formulation to construct a higher dimensional generalization of the action. Finally, for the (2+1)(2+1)-dimensional Chern–Simons theory we find solutions and interpret these as electric monopoles, analyze their charges and argue that the asymptotic symmetries are infinite-dimensional.