Generalized symmetries of topological field theories

Point Symmetries of Generalized Toda Field Theories II Applications of the Symmetries

The Lie symmetries of a large class of generalized Toda field theories are studied and used to perform symmetry reduction. Reductions lead to generalized Toda lattices on one hand, to periodic systems on the other. Boundary conditions are introduced to reduce theories on an infinite lattice to those on semi-infinite, or finite ones.

Topological Quantum Field Theories on Generalized Cobordism Categories

Balanced Topological Field Theories

We describe a class of topological field theories called “balanced topological field theories.” These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of “iterated superspaces” that carry two differentials. We find the ...

Topological Quantum Field Theories

We intruduce a new invariant for σ models (and foliations more generally) using the even pairing between K-homology and cyclic homology. We try to calculate it for the simplest case of foliations, namely principal bundles. We end up by discussing some possible physical applications primarily in Quantum Gravity and M-Theory. PACS classification: 11.10.-z; 11.15.-q; 11.30.-Ly

Topological Quantum Field Theories

Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of topological quantum field theories were constructed in my papers in late seventies) and I come to some new results, that were not published yet.