Nonlinear pole topology of slow currents in holographic probe-brane metals
Abstract
Low-frequency Drude response does not by itself determine which nearly conserved sector carries an electric current. We classify the leading cubic retarded response of an isolated, inversion-symmetric slow vector by its pole topology. Constitutive nonlinearity produces only incoming-frequency poles, whereas nonlinear relaxation adds a propagator at the emitted frequency; coupling to a second scalar slow mode generates pair-frequency poles. We then compute the full complex third-harmonic response of finite-density Dirac--Born--Infeld probe branes in Lifshitz black-brane backgrounds. In the marginal z=2 theory, the dense infrared response approaches the relaxation topology, with a signed infrared weight pIR=0.994±0.002 and a normalization-independent zero at ω×/ΓJ=0.2918. Nonmarginal z=1 and z=3/2 backgrounds instead realize mixed constitutive--relaxation weights, demonstrating that the topology is selected dynamically rather than imposed by the DBI square root. The exact nonlinear dc solution further yields a parameter-free dense-limit scaling function and a crossover field Enl∝ T3/2 at z=2. These results connect emergent higher-form slow currents, nonlinear response theory, and holographic transport, while the two-mode extension identifies the additional pole structures expected when energy or deformation modes remain slow.
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BibTeX
@misc{han2026nonlinear,
title = {{Nonlinear pole topology of slow currents in holographic probe-brane metals}},
author = {Yan Han and Xiang-Qian Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32748},
eprint = {2609.32748},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32748},
}
RIS
TY - UNPB
TI - Nonlinear pole topology of slow currents in holographic probe-brane metals
AU - Yan Han
AU - Xiang-Qian Li
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32748
UR - https://arxiv.org/abs/2609.32748
AB - Low-frequency Drude response does not by itself determine which nearly conserved sector carries an electric current. We classify the leading cubic retarded response of an isolated, inversion-symmetric slow vector by its pole topology. Constitutive nonlinearity produces only incoming-frequency poles, whereas nonlinear relaxation adds a propagator at the emitted frequency; coupling to a second scalar slow mode generates pair-frequency poles. We then compute the full complex third-harmonic response of finite-density Dirac--Born--Infeld probe branes in Lifshitz black-brane backgrounds. In the marginal z=2 theory, the dense infrared response approaches the relaxation topology, with a signed infrared weight p_IR=0.994±0.002 and a normalization-independent zero at ω_×/Γ_J=0.2918. Nonmarginal z=1 and z=3/2 backgrounds instead realize mixed constitutive--relaxation weights, demonstrating that the topology is selected dynamically rather than imposed by the DBI square root. The exact nonlinear dc solution further yields a parameter-free dense-limit scaling function and a crossover field E_nl∝ T^3/2 at z=2. These results connect emergent higher-form slow currents, nonlinear response theory, and holographic transport, while the two-mode extension identifies the additional pole structures expected when energy or deformation modes remain slow.
ER -