- The paper derives novel expressions for DC thermoelectric and thermal conductivities from black hole horizon data in systems with momentum dissipation.
- It uses holographic Q-lattice models and linear massless axions to simplify the transport calculations by reducing PDEs to ODEs.
- The findings offer practical insights into metallic versus insulating behavior and establish transport bounds in holographic dual frameworks.
Analysis of Thermoelectric DC Conductivities from Black Hole Horizons
The paper authored by Aristomenis Donos and Jerome P. Gauntlett provides a comprehensive extension of analytical methods to compute thermoelectric and thermal direct current (DC) conductivities of strongly coupled quantum field theories, specifically focusing on systems that exhibit momentum dissipation. Leveraging the holographic framework, the authors extend prior work on electrical conductivity by deriving analogous expressions for thermoelectric and thermal conductivities in terms of black hole horizon data.
This research begins with the acknowledgment of prior developments in calculating AC conductivities through retarded Green's functions, emphasizing the utility of holography for strongly coupled systems. This work generalizes the AC results by directly addressing DC responses, offering expressions that pave the way for deeper analysis of specific models where holographic techniques apply.
The authors focus on holographic Q-lattice models and linear massless axions to demonstrate their results. The Q-lattice models introduced in the paper break translation invariance by periodically varying scalar fields while preserving the homogeneity of the metric through the breaking of translational symmetry. This technical simplification allows for solving ordinary differential equations rather than partial differential equations, which is significant for the practical computation of conductivities.
Key results include the expressions for DC conductivities in terms of horizon data, which comprehensively consider isotropic and anisotropic cases in both four and five-dimensional bulk spacetime dimensions. The outcomes align with the intuition that in the presence of momentum dissipation mechanisms, as introduced by Q-lattices and massless axions, the DC conductivities achieve finiteness even as AC responses may diverge.
The implications of these results are multi-faceted. The paper provides a pathway to probe low-temperature scalings of DC conductivities, revealing whether ground states are metallic or insulating based on the electric and thermal transport properties. Additionally, it elucidates several bounds, such as the relationship between thermal and thermoelectric conductivities underlining universal behavior in certain conditions, applicable across dimensionalities and symmetries preserved by the holographic duals.
From a theoretical standpoint, such expressions create a robust connection to the transport properties predicted by memory matrix formalism, offering consistency with phenomenological models employed in condensed matter physics to describe complex materials lacking quasiparticle descriptions. Practically, this work emphasizes the relevance of holography in modeling strongly correlated electron systems, providing potentially valuable insights into novel materials such as strange metals and unconventional superconductors.
In conclusion, Donos and Gauntlett's work opens new avenues for the application of holographic methods to probe the transport phenomena in strongly coupled systems, highlighting its relevance in understanding complicated many-body quantum systems from a gravity dual perspective. Future developments in this direction may include extending these methods to incorporate more complex interactions, disorder effects, or external fields, to better mirror experimental realities. The paper sets a foundation for extending holographic models to other fields such as non-equilibrium dynamics and complex fluids, broadening the horizon of applications of string-theoretical methods in theoretical physics.