Conformal symmetry wormholes and the null energy condition

In this paper we seek a relationship between the assumption of conformal symmetry and the exotic matter needed to hold a wormhole open. By starting with a Morris-Thorne wormhole having a constant energy density, it is shown that the conformal factor provides the extra degree of freedom sufficient to account for the exotic matter. The same holds for Morris-Thorne wormholes in a noncommutative-geometry setting. Applied to thin shells, there would exist a radius that results in a wormhole with positive surface density and negative surface pressure and which violates the null energy condition on the thin shell.