Dimensional reduction, extended topological field theories and orbifoldization

Dimensional reduction of dual topological theories

We describe the reduction from four to two dimensions of the SU(2) Donaldson-Witten theory and the dual twisted Seiberg-Witten theory, i.e. the Abelian topological field theory corresponding to the Seiberg–Witten monopole equations. NBI-HE-96-14 hep-th/9603023 ∗E-mail: [email protected]

On 2-dimensional Topological Field Theories

Solitons in Two–dimensional Topological Field Theories

We consider a class of N = 2 supersymmetric non–unitary theories in two– dimensional Minkowski spacetime which admit classical solitonic solutions. We show how these models can be twisted into a topological sector whose energy–momentum tensor is a BRST commutator. There is an infinite number of degrees of freedom associated to the zero modes of the solitons. As explicit realizations of such mod...

2-dimensional Topological Quantum Field Theories and Frobenius Algebras

Category theory provides a more abstract and thus more general setting for considering the structure of mathematical objects. 2-dimensional quantum field theories arise in physics as objects that assign vector spaces to 1-manifolds and linear maps to 2-cobordisms. From a categorical perspective, we find that they are the same as commutative Frobenius algebras. Our main goal is to explain this e...

Two-dimensional Topological Quantum Field Theories and Frobenius Algebras

We characterize Frobenius algebras A as algebras having a comultiplication which is a map of A-modules. This characterization allows a simple demonstration of the compatibility of Frobenius algebra structure with direct sums. We then classify the indecomposable Frobenius algebras as being either \annihilator algebras" | algebras whose socle is a principal ideal | or eld extensions. The relation...