Noncommutative Frobenius algebras and open-closed duality

TL;DR

This paper explores the construction of noncommutative Frobenius algebras from symmetric group classes and their interpretation as open string theories, revealing connections to closed string theories through open-closed duality.

Contribution

It introduces a new class of noncommutative Frobenius algebras derived from symmetric group classes and relates their centers to closed string theories via open-closed duality.

Findings

Noncommutative Frobenius algebras can be constructed from symmetric group classes.

Centers of these algebras relate to closed string theories.

Area-dependent 2D field theories are analyzed.

Abstract

Some equivalence classes in symmetric group lead to an interesting class of noncommutive and associative algebras. From these algebras we construct noncommutative Frobenius algebras. Based on the correspondence between Frobenius algebras and two-dimensional topological field theories, the noncommutative Frobenius algebras can be interpreted as topological open string theories. It is observed that the centre of the algebras are related to closed string theories via open-closed duality. Area-dependent two-dimensional field theories are also studied.