Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 14 сентября 2013 г.
Аннотация: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 that are families (A, B(*). phi) where A = A(s)vertical bar is an element of S are families of commutative associative Frobenius algebras, B(*). = circle plus alpha epsilon Sigma B(alpha) is an associative algebra of Frobenius type graduated by graphs, and phi = phi(s)(alpha) : A(s) -> End(B(alpha))vertical bar S is an element of S, alpha is an element of Sigma is a family of special representations. Examples of cyclic foam topological field theories and graph-Cardy-Frobenius algebras are constructed. (C) 2010 Elsevier B.V. All rights reserved.