Hidden global conformal symmetry without Virasoro extension in theory of elasticity

Abstract

The theory of elasticity (a.k.a. Riva-Cardy model) has been regarded as an example of scale invariant but not conformal field theories. We argue that in $d=2$ dimensions, the theory has hidden global conformal symmetry of $SL(2,\mathbb{R}) \times SL(2,\mathbb{R})$ without its Virasoro extension. More precisely, we can embed all the correlation functions of the displacement vector into a global conformal field theory with four-derivative action in terms of two scalar potential variables, which necessarily violates the reflection positivity. The energy-momentum tensor for the potential variables cannot be improved to become traceless so that it does not show the Virasoro symmetry even with the existence of global special conformal current.