Abstract
We study models of translational symmetry breaking in which inhomogeneous matter field profiles can be engineered in such a way that black brane metrics remain isotropic and homogeneous. We explore novel Lagrangians involving square root terms and show how these are related to massive gravity models and to tensionless limits of branes. Analytic expressions for the DC conductivity and for the low frequency scaling of the optical conductivity in phenomenological models are derived, and the optical conductivity is studied in detail numerically. The square root Lagrangians are associated with linear growth in the DC resistivity with temperature and also lead to minima in the optical conductivity at finite frequency, suggesting that our models may capture many features of heavy fermion systems.
Highlights
The simplest models of explicit translational symmetry breakingWe consider an Einstein–Maxwell model with cosmological constant, coupled to matter, i.e. an action
From this Ward identity it is evident that one can generically violate momentum conservation, while preserving energy density conservation, by introducing background sources in the field theory which depend on the spatial coordinates. (Note that spontaneous breaking of the translational symmetry on its own is not enough to dissipate momentum.)
We explore the low frequency behaviour of the optical conductivity at low temperature, finding that for all values of our parameters there is a peak at zero frequency, indicating metallic behaviour
Summary
We consider an Einstein–Maxwell model with cosmological constant, coupled to matter, i.e. an action. We will consider matter actions which are scalar functionals of the following form: S(M) =. The stress energy tensor associated with the scalar matter is given by. Evaluated on the solution above, this stress energy tensor is by construction homogeneous but not spatially isotropic. Consider a matter action which is a multi-scalar functional of the following form: dd. A special case in which spatial isotropy is restored is the following: choose all (d − 1) scalar Lagrangians to take the same functional form. By choosing cI = cxa, i.e. cIa = c we obtain a stress energy tensor which restores rotational symmetry in the spatial directions:. Given any Lagrangian functional built out of (d − 1) scalar fields with shift symmetry, one can construct solutions for which the stress energy tensor preserves spatial isotropy and homogeneity. In the remainder of this section we will consider the physical interpretations of various types of functionals
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