On invertible $2$-dimensional framed and $r$-spin topological field theories

On 2-dimensional Topological Field Theories

Spin Topological Quantum Field Theories

Starting from the quantum group Uq(sl(2, C)), we construct operator invariants of 3-cobordisms with spin structure, satisfying the requirements of a topological quantum field theory and refining the Reshetikhin–Turaev and Turaev–Viro models. We establish the relationship between these two refined models.

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...

Integrable Systems and Classification of 2 - Dimensional Topological Field Theories

In this paper we consider from the point of view of differential geometry and of the theory of integrable systems the so-called WDVV equations as defining relations of 2-dimensional topological field theory. A complete classification of massive topological con-formal field theories (TCFT) is obtained in terms of monodromy data of an auxillary linear operator with rational coefficients. Procedur...

Sl(2,r) Chern-simons Theories with Rational Charges and 2-dimensional Conformal Field Theories

We present a hamiltonian quantization of the SL(2, R) 3-dimensional ChernSimons theory with fractional coupling constant k = s/r on a space manifold with torus topology in the “constrain-first” framework. By generalizing the “Weyl-odd” projection to the fractional charge case, we obtain multi-components holomorphic wave functions whose components are the Kac-Wakimoto characters of the modular i...