Lattice topological field theory in two dimensions

Lattice Versions of Quantum Field Theory Models in Two Dimensions

Lattice Supersymmetry and Topological Field Theory

We discuss the connection between supersymmetric field theories and topological field theories and show how this connection may be used to construct local lattice field theories which maintain an exact supersymmetry. It is shown how metric independence of the continuum topological field theory allows us to derive the lattice theory by blocking out of the continuum in a deformed geometry. This, ...

Quasi-Topological Field Theories in Two Dimensions as Soluble Models

We study a class of lattice field theories in two dimensions that includes gauge theories. Given a two dimensional orientable surface of genus g, the partition function Z is defined for a triangulation consisting of n triangles of area ǫ. The reason these models are called quasi-topological is that Z depends on g, n and ǫ but not on the details of the triangulation. They are also soluble in the...

The Classification of Topological Quantum Field Theories in Two Dimensions

The goal of this thesis is to introduce some of the major ideas behind extended topological quantum field theories with an emphasis on explicit examples and calculations. The statement of the Cobordism Hypothesis is explained and immediately used to classify framed and oriented extended 2 dimensional topological quantum field theories. The passage from framed theories to oriented theories is eq...

On the structure of open-closed topological field theory in two-dimensions

I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal’s geometric axioms. Exploiting the topological sewing constraints allows for the identification of the algebraic structure governing such systems. I give a careful treatment of bulk-boundary and boundary-bulk correspondences, which a...