Confinement and domain walls in high density quark matter

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In this talk I will review some recent progress in our understanding of properties of high density quark matter. This talk is based mainly on the papers hep-ph/0011379, hep-ph/0012041, hep-ph/0108260, and cond-mat/0103451, done in collaboration with D. Rischke, M. Stephanov, and A. Zhitnitsky.
6 pages. Talk at the Conference on Compact Stars in the QCD Phase Diagram, Copenhagen, (Aug. 15-18, 2001)

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