## Abstract

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 language | English (US) |
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Article number | 144001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 52 |

Issue number | 14 |

DOIs | |

State | Published - 2019 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

## Keywords

- Riemann surfaces
- extended objects
- quantum field theory