A Chern-Simons theory for dipole symmetry

Abstract

We present effective field theories for dipole symmetric topological matters that can be described by the Chern-Simons theory. Unlike most studies using higher-rank gauge theory, we develop a framework with both U(1)U(1) and dipole gauge fields. As a result, only the highest multipole symmetry can support the ’t Hooft anomaly. We show that with appropriate point group symmetries, the dipolar Chern-Simons theory can exist in any dimension and, moreover, the bulk-edge correspondence can depend on the boundary. As two applications, we draw an analogy between the dipole anomaly and the torsional anomaly and generalize particle-vortex duality to dipole phase transitions. All of the above are in the flat spacetime limit, but our framework is able to systematically couple dipole symmetry to curved spacetime. Based on that, we give a proposal about anomalous dipole hydrodynamics. Moreover, we show that the fracton-elasticity duality arises naturally from a non-abelian Chern-Simons theory in 3D.

Carroll black holes

“…The result for the Carrollian temperature (172) is equivalent to the corresponding Lorentzian result for the Hawking temperature of 2d dilaton gravity with the same potentials (16).…”

“…Finally, we come back to more general cases when the potential V does not only depend on the dilaton X but additionally depends on the boost invariant scalar X H . We discuss here the family of models (16) and refer by analogy to [64] for further generalizations.…”

“…If we insist on a metric BF theory, which would be closer to Carroll/dipole Chern-Simons gravity [16,17], we can add two nontrivial central extensions, in which case the dipole algebra admits an invariant metric [43]. This can also be generalized [43] to nontrivial cosmological constant [12,13] or to more general gravitational models.…”

“…Indeed, Carroll symmetries emerge naturally on null surfaces and therefore find their place at null infinity [4], at black hole horizons [5][6][7], but also at spatial [8] and time-like infinity [9] in the extreme situation that one direction decouples. Due to its restricted mobility, Carrollian physics shares features with fractons [10][11][12][13] (more precisely, particles with conserved electric charge and dipole moment) and is relevant in models with so-called "spacetime subsymmetries" [14,15] (see also [16,17]). Another condensed matter application of Carroll symmetries is flat bands [18] (the Fourier-transformed statement of collapsed lightcones).…”