When duality changes the poles: SL(2,ℤ) transformations of linear response EFTs
Abstract
We study how SL(2,ℤ) transformations act on pole-truncated linear-response effective theories in (2+1) dimensions. For correlators meromorphic within a finite low-frequency domain, the EFT data include both derivative-expanded transport coefficients and the retained non-hydrodynamic poles. Since the S-transformation inverts the optical conductivity and exchanges its poles and zeros, it does not necessarily commute with the infrared truncation. We derive explicit maps for static susceptibilities, the Einstein relation and AC transport coefficients. In the purely hydrodynamic sector the map closes on the original transport data, while in quasihydrodynamic regimes the transformed pole positions and, in general, residues constitute additional infrared data. We test the construction in the alternatively quantised D3/D5 probe-brane system, where an EFT retaining one original gapped pole can correspond to transformed EFTs retaining zero, one or two. The holographic results verify the analytic maps and exhibit an inverse-Drude conductivity at large values of the control parameter.
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BibTeX
@misc{amoretti2026when,
title = {{When duality changes the poles: $SL(2,\mathbbZ)$ transformations of linear response EFTs}},
author = {Andrea Amoretti and Daniel K. Brattan and Jonas Rongen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19075},
eprint = {2609.19075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19075},
}
RIS
TY - UNPB
TI - When duality changes the poles: SL(2,ℤ) transformations of linear response EFTs
AU - Andrea Amoretti
AU - Daniel K. Brattan
AU - Jonas Rongen
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.19075
UR - https://arxiv.org/abs/2609.19075
AB - We study how SL(2,ℤ) transformations act on pole-truncated linear-response effective theories in (2+1) dimensions. For correlators meromorphic within a finite low-frequency domain, the EFT data include both derivative-expanded transport coefficients and the retained non-hydrodynamic poles. Since the S-transformation inverts the optical conductivity and exchanges its poles and zeros, it does not necessarily commute with the infrared truncation. We derive explicit maps for static susceptibilities, the Einstein relation and AC transport coefficients. In the purely hydrodynamic sector the map closes on the original transport data, while in quasihydrodynamic regimes the transformed pole positions and, in general, residues constitute additional infrared data. We test the construction in the alternatively quantised D3/D5 probe-brane system, where an EFT retaining one original gapped pole can correspond to transformed EFTs retaining zero, one or two. The holographic results verify the analytic maps and exhibit an inverse-Drude conductivity at large values of the control parameter.
ER -