A new kind of quantum field theory of (n - 1)-dimensional defects in 2n dimensions

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I describe a project to open a new territory of quantum field theory where the fields live not on a space-time manifold but on certain complete metric spaces of (n - 1)-dimensional objects (defects) in a 2n-dimensional space-time M. These metric spaces are 'quasi Riemann surfaces'; they are formally analogous to Riemann surfaces. Every construction of a 2d conformal field theory (CFT) is to give an analogous construction of a CFT on the quasi Riemann surfaces, and thereby a cft on M. The global symmetry group of the 2d CFT becomes a local gauge symmetry. Ordinary local quantum fields in space-time are constructed by restricting to small objects. The project is based on writing the free n-form in 2n dimensions as the 2d Gaussian model on the quasi Riemann surfaces.

Original languageEnglish (US)
Article number144001
JournalJournal of Physics A: Mathematical and Theoretical
Issue number14
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


  • Riemann surfaces
  • extended objects
  • quantum field theory


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