The theory of symmetric tensor field: from fractons to gravitons and back

TL;DR

This paper explores a symmetric tensor field theory in 4D with a unique gauge symmetry that bridges fractons and gravitons, revealing a continuous transition between these phases and analyzing the implications for propagator behavior.

Contribution

It introduces a novel gauge symmetry weaker than diffeomorphism invariance, enabling a continuous transition between linearized gravity and fracton phases without changing degrees of freedom.

Findings

The theory depends on a dimensionless parameter affecting its properties.

Propagators are computed and constrained to be tachyonic-free in the massive case.

A special parameter value leads to a non-propagating phase related to fractons.

Abstract

We consider the theory of a symmetric tensor field in 4D, invariant under a subclass of infinitesimal diffeomorphism transformations, where the vector diff parameter is the 4-divergence of a scalar parameter. The resulting gauge symmetry characterizes the "fracton" quasiparticles and identifies a theory which depends on a dimensionless parameter, which cannot be reabsorbed by a redefinition of the tensor field, despite the fact that the theory is free of interactions. This kind of "electromagnetic gauge symmetry" is weaker that the original diffeomorphism invariance, in the sense that the most general action contains, but is not limited to, linearized gravity, and we show how it is possible to switch continuously from linearized gravity to a mixed phase where both gravitons and fractons are present, without changing the degrees of freedom of the theory. The gauge fixing procedure is particularly rich and rather peculiar, and leads to the computation of propagators which in the massive case we ask to be tachyonic-free, thus constraining the domain of the parameter of the theory. Finally, a closer contact to fractons is made by the introduction of a parameter related to the "rate of propagation". For a particular value of this parameter the theory does not propagate at all, and we guess that, for this reason, the resulting theory should be tightly related to the fracton excitations.