Abstract
We generalize current holographic models with homogeneous breaking of translation symmetry by incorporating higher derivative couplings, in the spirit of effective field theories. Focusing on charge transport, we specialize to two simple couplings between the charge and translation symmetry breaking sectors. We obtain analytical charged black brane solutions and compute their DC conductivity in terms of horizon data. We constrain the allowed values of the couplings and note that the DC conductivity can vanish at zero temperature for strong translation symmetry breaking, thus showing that in general there is no lower bound on the conductivity.
Highlights
Background solutionIn this case, the action is simplified as S = M 2 d4 + V (X ) 1 4 Fμν F μν J 4 Tr[X F 2] (3.1)For simplicity, we set the Planck scale M = 1 in appropriate units
We constrain the allowed values of the couplings and note that the DC conductivity can vanish at zero temperature for strong translation symmetry breaking, showing that in general there is no lower bound on the conductivity
We have expanded on previous modelisations of holographic homogeneous translation symmetry breaking and charge transport by going beyond the leading lowenergy two-derivative terms in the action
Summary
We will construct here general effective actions for momentum relaxation in the limit in which the effects are smeared over all distances. That traces of the tensors like Tr[Xn] ≡ (Xn)μμ are scalars. We will include these in Einstein-Maxwell-Dilaton (EMD) theories. The effective action in this case is obtained from (2.6)–(2.10) by taking all functions of φ to be φ-independent. We are going to focus on two examples that have not yet been studied in the literature, keeping V (X) general for : the axions XI couple directly to the kinetic term of the U(1) gauge boson either with.
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