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

TL;DR

This paper proposes a novel quantum field theory framework where fields are defined on (n-1)-dimensional defects within 2n-dimensional space, using quasi Riemann surfaces to generalize 2D conformal field theories.

Contribution

It introduces a new class of quantum field theories on defect spaces, extending 2D conformal field theory concepts to higher dimensions via quasi Riemann surfaces.

Findings

Construction of quantum fields on defect spaces

Analogy between quasi Riemann surfaces and Riemann surfaces

Extension of 2D CFT techniques to higher dimensions

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 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. This note is a summary of the main points of arXiv:1605.03279.