A relativistic non-perturbative local model of fractons and its non-local perturbative hidden sector

Abstract

We construct, from first principles, a covariant local model for scalar fractonic matter coupled to a symmetric tensor gauge field. The free gauge field action is just the one of the Blasi-Maggiore model. The scalar sector, describing fracton charges, is a non-trivial covariant generalization of Pretko's quartic model. Because the model has no quadratic term in the scalar field, a direct perturbative treatment fails. Remarkably, by performing a suitable change of variables, we demonstrate that the action can be driven to a perturbative effective action. However, at the price of carrying non-local interacting terms. We study the perturbative regime of the model first by analyzing the classical field equations and some possible simple solutions, which are in accordance with the expected immobile behavior of fractons. We also derive the fracton dispersion relation and, by playing with the parameters of the model, show that there are at least six distinct phases: one with two massive fractonic modes, one of them being tachyonic; one with massless states associated with a long-range attractive potential; a mixed phase with one massive and one massless state; another one where physical states of the scalar field cannot occur at all in the physical spectrum; a massive phase with states of two different masses; and second phase where the scalar field cannot be associated with physical particles, in spite of its mass being real. Moreover, we find evidence that fractonic bound states emerge in the model for some of these phases.