Special Legendrian submanifolds in toric Sasaki-Einstein manifolds

We show every toric Sasaki-Einstein manifold S admits a special Legendrian submanifold L which arises as the link fix(tau) boolean AND S of the fixed point set fix(tau) of an anti-holomorphic involution tau on the cone C(S). In particular, we obtain a special Legendrian torus S-1 x S-1 in an irregular toric Sasaki-Einstein manifold which is diffeomorphic to S-2 x S-3. Moreover, there exists a special Legendrian submanifold in #m(S-2 x S-3) for each m >= 1.