Conformal Field Theory of Critical Casimir Interactions in 2D

TL;DR

This paper derives an exact conformal field theory-based formula for the critical Casimir interaction between arbitrarily shaped objects in 2D, revealing a universal geometric component tied to conformal charge.

Contribution

It introduces a novel exact method to compute 2D critical Casimir forces for arbitrary shapes using conformal field theory principles.

Findings

Exact expression for Casimir interaction in 2D CFTs

Identification of a shape-dependent geometric energy component

Universal dependence on conformal charge and shape, independent of boundary conditions

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.