Cyclic Foam Topological Field Theories

Abstract

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 $(A,B_{\star },\varphi )$, where $A=\{A^s|s\in S\}$ are families of commutative associative Frobenius algebras, $B_{\star }={⨁}_{\sigma \in \Sigma }{B}_{\sigma }$ is an graduated by graphes, associative algebras of Frobenius type and $\varphi =\{{\varphi }_{\sigma }^s:A^s\to (B_{\sigma })|s\in S,\sigma \in \Sigma \}$ is a family of special representations. There are constructed examples of Cyclic Foam Topological Field theories and its graph-Cardy-Frobenius algebras

14 pages

References in corpus (5)

• D-branes and K-theory in 2D topological field theory
• The universal sl3-link homology
• Spin Foam Models of Quantum Spacetime
• Classification of Supersymmetric Flux Vacua in M Theory
• Formal Homotopy Quantum Field Theories, I: Formal Maps and Crossed C-algebras

Cited by in corpus (5)

• Infinite tri-symmetric group, multiplication of double cosets, and checker topological field theories
• Klein Topological Field Theories from Group Representations
• Infinite symmetric group and combinatorial descriptions of semigroups of double cosets
• Integrals of tau functions
• Brane Topological Field Theories and Hurwitz numbers for CW-complexes