The main result of this paper is the construction of a conformally covariant operator in two dimensions acting on scalar fields and containing fourth order derivatives. In this way it is possible to derive a class of Lagrangians invariant under conformal transformations. They define conformal field theories satisfying equations of the biharmonic type. Two kinds of these biharmonic field theorie...

To a domain wall or string object, Noether charge and topological spatial objects can be attracted, forming a composite BPS (Bogomolny-Prasad-Sommerfield) object. We consider two field theories and derive a new BPS bound on composite linear solitons involving multiple charges. Among the BPS objects ‘supertubes’ appear when the wall or string tension is canceled by the bound energy, and could ta...

In this short note we provide a review of some developments in the area of homotopy quantum field theories, loosely based on a talk given by the second author at the Xth Oporto Meeting on Geometry, Topology and Physics. Homotopy Quantum Field Theories Homotopy quantum field theories were invented by Turaev [10], though the idea goes back to Segal’s discussion of the possible geometry underlying...

Three lectures in which I give an introduction to effective field theories in particle physics.

All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories, i.e., gauged Wess-ZuminoWitten (WZW) models with compact gauge groups. In this paper we use subfactor theory and ideas of algebraic quantum field theory to approach coset Conformal Field Theories. Two conjectures are formulated and their consequences are discussed. Some ...

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

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.

An effective field theory (EFT) of a physical system is a theory of the dynamics of the system at energies small compared to a given cutoff. For some systems, low-energy states with respect to this cutoff are effectively independent of ("decoupled from") states at high energies. Hence one may study the low-energy sector of the theory without the need for a detailed description of the high-energ...

A minimal area problem imposing different length conditions on open and closed curves is shown to define a one parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten’s open string field theory capable of incorporating on shell closed strings. The string diagrams of th...