Cyclic Foam Topological Field Theories

Details Cyclic Foam Topological Field Theories Cyclic Foam Topological Field Theories

2007-12-20

arxiv.org/abs/0712.3557v3

J.Geom.Phys.60:874-883,2010

Mathematics

Geometric Topology

14 pages

Scientific paper

10.1016/j.geomphys.2010.02.004

This paper proposes an axiomatic 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 two-manifolds with one-dimensional singularities. We proved that Cyclic Foam Topological Field theories one-to-one correspond to graph-Cardy-Frobenius algebras, that are families $(A,B_\star,\phi)$, where $A=\{A^s|s\in S\}$ are families of commutative associative Frobenius algebras, $B_\star = \bigoplus_{\sigma\in\Sigma} B_\sigma$ is an graduated by graphes, associative algebras of Frobenius type and $\phi=\{\phi_\sigma^s: A^s\to (B_\sigma)|s\in S,\sigma\in \Sigma\}$ is a family of special representations. There are constructed examples of Cyclic Foam Topological Field theories and its graph-Cardy-Frobenius algebras

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