[Paper Review] Momentum dissipation and holographic transport without self-duality

Jian-Pin Wu|arXiv (Cornell University)|Sep 15, 2016

Black Holes and Theoretical Physics86 references3 citations

TL;DR

This paper studies holographic transport in a strongly coupled conformal field theory (CFT) with momentum dissipation via spatial linear axionic fields, breaking electromagnetic self-duality through Weyl tensor coupling to the Maxwell field. For γ > 0, momentum dissipation drives the system into an incoherent metallic phase with a conductivity dip, while γ < 0 yields a peak; a specific α̂ value renders DC conductivity, diffusion constant, and susceptibility independent of γ, and at this α̂, particle-vortex duality holds best under γ sign flip.

ABSTRACT

We implement the momentum dissipation introduced by spatial linear axionic fields in a holographic model without self-duality, broke by Weyl tensor coupling to Maxwell field, and study its response. It is found that for the positive Weyl coupling parameter $γ&gt;0$, the momentum dissipation characterized by parameter $\hatα$ drives the boundary conformal field theory (CFT), in which the conductivity exhibits a peak at low frequency, into the incoherent metallic phase with a dip, which is away from CFT due to the introduction of axionic fields. While for $γ&lt;0$, an oppositive scenario is found. Our present model provides a possible route toward the problem that which sign of $γ$ is the correct description of the CFT of boson Hubbard model. In addition, we also investigate the DC conductivity, diffusion constant and susceptibility. We find that for each of these observables there is a specific value of $\hatα$, for which these observables are independent of $γ$. Finally, the electromagnetic (EM) duality is also studied and we find that there is also a specific value of $\hatα$, for which the particle-vortex duality related by the change of the sign of $γ$ in the boundary theory holds better than for other values of $\hatα$.

Motivation & Objective

• To study momentum dissipation in a holographic CFT without EM self-duality, using axionic fields and Weyl-Maxwell coupling.
• To determine how the sign of the Weyl coupling parameter γ affects optical conductivity and transport behavior.
• To identify conditions under which DC conductivity, diffusion constant, and susceptibility become independent of γ.
• To investigate the validity of particle-vortex duality under γ sign flip and its dependence on momentum dissipation strength α̂.
• To assess the stability of the system across different γ and α̂ values via quasinormal mode analysis.

Proposed method

• Introduce momentum dissipation via spatially linear axionic scalar fields Φ_I in a 4D bulk with a Schwarzschild-AdS black brane.
• Couple the Maxwell field to the Weyl tensor via a γ-dependent interaction term in the action, breaking EM self-duality.
• Solve the linearized equations of motion for vector perturbations (A_t, A_y) to compute the optical conductivity and transport coefficients.
• Use the WKB approximation to analyze potential wells and bound states, ensuring absence of unstable quasinormal modes.
• Compute the DC conductivity, diffusion constant, and magnetic susceptibility numerically across varying α̂ and γ.
• Analyze the behavior of the effective potential V_i(u) for longitudinal and transverse modes to assess stability across γ ∈ S₀ and α̂ > 0.

Experimental results

Research questions

• RQ1 How does the sign of the Weyl coupling parameter γ affect the low-frequency optical conductivity in the presence of momentum dissipation?
• RQ2 At what value of the momentum dissipation parameter α̂ do DC conductivity, diffusion constant, and susceptibility become independent of γ?
• RQ3 Does particle-vortex duality, related by γ → -γ, hold better at a specific α̂ value in this non-self-dual model?
• RQ4 Can the system remain stable (no unstable modes) for γ beyond the self-dual region S₀ when momentum dissipation is introduced?
• RQ5 How does momentum dissipation affect the stability of the effective potential for vector modes across different momentum regimes?

Key findings

• For γ > 0, momentum dissipation via α̂ drives the system into an incoherent metallic phase with a conductivity dip, distinct from the original CFT.
• For γ < 0, the optical conductivity exhibits a peak at low frequency, resembling quasi-particle behavior.
• At a specific α̂ value, the DC conductivity, diffusion constant, and magnetic susceptibility become independent of the Weyl coupling parameter γ.
• The particle-vortex duality under γ → -γ is most robust at this same critical α̂ value, where duality symmetry is best preserved.
• The system remains stable across γ ∈ S₀ even with momentum dissipation, and the viable region for stability may widen beyond S₀ when α̂ ≠ 0.
• No unstable quasinormal modes are found in the small or finite momentum regimes, as confirmed by WKB analysis of bound states with ñ₁t < 1.