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We report the infrared (IR) response of Cu-O chains in the high-$T_{c}$superconductor YBa$_{2}$Cu$_{3}$O$_{y}$ over the doping range spanning $%y=6.28-6.75$. We find evidence for a power law scaling at mid-IR frequenciesconsistent with predictions for Tomonaga-Luttinger liquid, thus supporting thenotion of one-dimensional transport in the chains. We analyze the role ofcoupling to the CuO$_{2}$ planes in establishing metallicity andsuperconductivity in disordered chain fragments.Comment: 4 pages, 3 figure

physical review letters

Coherence and Superconductivity in Coupled One-Dimensional Chains: A Case Study of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>YBa</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Cu</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:math>

Coherence and Superconductivity in Coupled One-Dimensional Chains: A Case Study ofYBa2Cu3Oy