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Article

Cyclic Foam Topological Field Theories

Journal of Geometry and Physics. 2010. Vol. 60. No. 6-8. P. 874-883.

This paper proposes an axiomatic form for cyclic foam topological field theories, that is topological field theories corresponding to string theories, where particles are arbitrary graphs. World surfaces in this case are 2-manifolds with one-dimensional singularities. I prove that cyclic foam topological field theories are in one-to-one correspondence with graph-Cardy-Frobenius algebras. Examples of cyclic foam topological field theories and graph-Cardy-Frobenius algebras are constructed.