Hidden global conformal symmetry without Virasoro extension in theory of   elasticity
  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. 
Yu Nakayama
hep-th cond-mat.stat-mech math-ph math.MP