Four dimensional Conformal field theories (CFT4) from two dimensional topological field theories (TFT2) and polynomial rings.

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Recent research has established that all the correlators of local operators in free four dimensional scalar field theory can be formulated as amplitudes in a two-dimensional topological field theory. The description of the state space involves the construction of primary fields using polynomial rings. The mathematics of TFT2 and polynomial rings will be used to describe more general conformal field theories, and to compute the structure constants in these CFTs.