Quantum field theories of extended objects
This is a project to construct a new class of quantum field theories of (n−1)-dimensional extended objects (defects) in d=2n space-time dimensions.
For each ordinary 2d QFT, there is to be a corresponding new QFT of (n−1)-dimensional extended objects in any 2n-dimensional space-time manifold M.
The quantum fields live on “quasi Riemann surfaces”, which are certain complete metric spaces of integral (n−1)-currents in M. These quasi Riemann surfaces have analytic properties analogous to ordinary Riemann surfaces.
The new QFTs are to be constructed on the quasi Riemann surfaces just as ordinary 2d QFTs are constructed on ordinary Riemann surfaces.
The global symmetry group of the ordinary 2d QFT becomes the gauge group of a local gauge symmetry in the new QFT.
Papers
- Quasi Riemann surfaces (November 23, 2018) — draft of a short note aimed at mathematicians
- A new kind of quantum field theory of (n−1)-dimensional defects in 2n dimensions (November 13, 2017) — a 7 page summary
- Quantum field theories of extended objects (May 11, 2016)
Talks
- A new kind of quantum field theory of (n−1)-dimensional objects in 2n dimensions (January 16, 2018) — seminar, University of Amsterdam
- A new kind of quantum field theory of (n−1)-dimensional defects in 2n dimensions (September 8, 2017) — seminar, Chicheley Hall, UK
- Two notes aimed at mathematicians:
- Quasi Riemann surfaces (September 2, 2017)
- Quasi Riemann surfaces II. Questions, comments, speculations (September 2, 2017)
- Two talks on quantum field theories of extended objects (February 7–8, 2017) — seminars in Israel