  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.
