Abstract
We disclose the effects of the logarithmic nonlinear electrodynamics on the holographic conductivity of Lifshitz dilaton black holes/branes. We analyze thermodynamics of these solutions as a necessary requirement for applying gauge/gravity duality, by calculating conserved and thermodynamic quantities such as the temperature, entropy, electric potential and mass of the black holes/branes. We calculate the holographic conductivity for a $(2+1)$-dimensional brane boundary and study its behavior in terms of the frequency per temperature. Interestingly enough, we find out that, in contrast to the Lifshitz-Maxwell-dilaton black branes which has conductivity for all $z$, here in the presence of nonlinear gauge field, the holographic conductivity do exist provided $z\leq3$ and vanishes for $z>3$. It is shown that independent of the nonlinear parameter $\beta$, the real part of the conductivity is the same for a specific value of frequency per temperature in both AdS and Lifshitz cases. Besides, the behavior of real part of conductivity for large frequencies has a positive slope with respect to large frequencies for a system with Lifshitz symmetry whereas it tends to a constant for a system with AdS symmetry. This behavior may be interpreted as existence of an additional charge carrier rather than the AdS case, and is due to the presence of the scalar dilaton field in model. Similar behavior for optical conductivity of single-layer graphene induced by mild oxygen plasma exposure has been reported.
Highlights
The idea of correspondence between gravity in an anti-de Sitter (AdS) spaces and a conformal field theory (CFT) living on its boundary (AdS/CFT) [1,2,3] have been successful in many theories like superconductors, quark-gluon plasma and entanglement entropy
It has been well established that the gauge/gravity duality provides powerful tools for exploring dynamics of strongly coupled field theories and physics of our real Universe
An interesting application of gauge/gravity duality in condensed matter physics was suggested by Hartnoll, et al [4, 5] who demonstrated that some properties of strongly coupled superconductors have dual gravitational descriptions
Summary
The idea of correspondence between gravity in an anti-de Sitter (AdS) spaces and a conformal field theory (CFT) living on its boundary (AdS/CFT) [1,2,3] have been successful in many theories like superconductors, quark-gluon plasma and entanglement entropy. In the framework of dilaton gravity, thermal stability and thermodynamic geometry of a class of black hole spacetimes in the presence of logarithmic nonlinear electrodynamics have been explored in four [27] and higher dimensional spacetime [28]. We would like to consider a class of asymptotically Lifshitz black hole/brane solutions of Einstein-dilaton gravity in the presence of logarithmic nonlinear electrodynamics and study the thermodynamics of them as a necessary requirement for a system on which we intend to apply gauge/gravity duality. We introduce the action and construct a new class of asymptotic Lifshitz black hole/brane solutions of Einstein-dilaton gravity in the presence of logarithmic nonlinear electrodynamics. We finish our paper with concluding remarks in the last section
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