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

TL;DR

This paper constructs physical states of a non-critical 3-brane using 4D conformal field theory techniques on R*S^3, identifying invariant building blocks under conformal transformations.

Contribution

It introduces a systematic method to build and classify physical states of a non-critical 3-brane using conformal invariance on R*S^3.

Findings

Explicit construction of scalar, vector, and gravitational building blocks.

Classification of these building blocks into finite types.

Demonstration of invariance under conformal charges.

Abstract

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.