Conformal Field Theory of Critical Casimir Interactions in 2D

Abstract

Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two dimensional (2D) conformal field theories (CFT) we derive an exact result for the Casimir interaction between two objects of arbitrary shape, in terms of (1) the free energy of a circular ring whose radii are determined by the mutual capacitance of two conductors with the objects' shape; and (2) a purely geometric energy that is proportional to conformal charge of the CFT, but otherwise super-universal in that it depends only on the shapes and is independent of boundary conditions and other details.

5 pages, 3 figures

References in corpus (4)

• Critical Casimir forces in colloidal suspensions on chemically patterned surfaces
• Effective forces between colloids at interfaces induced by capillary wave-like fluctuations
• Critical Casimir torques and forces acting on needles in two spatial dimensions
• Scattering Approach for Fluctuation--Induced Interactions at Fluid Interfaces

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• The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants
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• Two-dimensional critical systems with mixed boundary conditions: Exact Ising results from conformal invariance and boundary-operator expansions
• Measurement-Induced Entanglement in Conformal Field Theory
• Reversing the Critical Casimir force by shape deformation