Building Blocks of Physical States in a Non-Critical 3-Brane on R*S³

The physical states in a world-volume model of a non-critical 3-brane are systematically constructed using techniques of four-dimensional conformal field theories on R*S^3 developed recently. Invariant combinations of creation modes under a special conformal transformation provide building blocks of physical states. Any state can be created by acting with such building blocks on a conformally invariant vacuum in an invariant way under the other conformal charges: the Hamiltonian and rotation generators on S^3. We explicitly construct building blocks for scalar, vector and gravitational fields, and classify them as finite types.