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When duality changes the poles: $SL(2,\mathbb{Z})$ transformations of linear response EFTs
We study how $SL(2,\mathbb Z)$ 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 pole
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