Parallel Transport along Closed Loop Doesn't Meet!
	Blue Phase Parallel Transport has Negative Curvature in Flat Space Rijij = -6 q^2

On sphere of radius 1/q in four dimensions, the curvature vanishes! There is an ideal template for double-twist there: n(x) = q(-x1, x0, x3, -x2)

The Blue Phase is like a carpet made of orange peel (figure copyright Pamela Davis Kivelson): the edges of the cuts are the defect lines.

• The Blue Phases: Introduction
• What Are Liquid Crystals?
• Order Parameter Fields
• Defects in Nematic Liquids
• Homotopy Theory and Defects
• Parallel Transport and Energy
• Twisted Parallelism: Chiral Nematics
• Chiral Nematic Phases: Helical and Blue
• Blue Phases: Networks of Defect Lines
• Defect Lines and Frustration: Curved Space

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Sethna's Research 90-94

Entertaining Science done at

LASSP.

James P. Sethna, sethna@lassp.cornell.edu

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).