Weyl corrections to holographic conductivity

TL;DR

This work examines how leading bulk Weyl-type higher-derivative corrections, encoded by a dimension-six operator with coefficient γ, modify transport in holographic CFTs. By combining the membrane paradigm and Minkowski AdS/CFT calculations, it shows that the canonical universal relation between DC conductivity, charge susceptibility, and temperature is violated at order γ, with explicit corrections to σ and the diffusion constant D in several spacetime dimensions (e.g., in d=4: σ = (π L T / g_5^2)(1 + 8 γ/L^2) and D = (1/(2π T))(1 + 16 γ/L^2)). The analysis also derives causality-based bounds on γ (roughly −L^2/16 < γ < L^2/24), illustrating how boundary causality constrains bulk effective field theories and their transport properties. Overall, the paper demonstrates controlled departures from universality due to higher-derivative bulk terms and connects these corrections to fundamental consistency conditions in holography.

Abstract

For conformal field theories which admit a dual gravitational description in anti-de Sitter space, electrical transport properties, such as conductivity and charge diffusion, are determined by the dynamics of a U(1) gauge field in the bulk and thus obey universality relations at the classical level due to the uniqueness of the Maxwell action. We analyze corrections to these transport parameters due to higher-dimension operators in the bulk action, beyond the leading Maxwell term, of which the most significant involves a coupling to the bulk Weyl tensor. We show that the ensuing corrections to conductivity and the diffusion constant break the universal relation with the U(1) central charge observed at leading order, but are nonetheless subject to interesting bounds associated with causality in the boundary CFT.