Chirality in 2d pAQFT

TL;DR

This paper develops a framework within perturbative algebraic quantum field theory to identify and analyze chiral subalgebras in 2-dimensional quantum field theories on curved spacetimes, demonstrating their independence from Cauchy surface choices.

Contribution

It explicitly constructs chiral subalgebras in 2d pAQFT, showing their covariant nature and independence from Cauchy surface choices, advancing understanding of chiral structures in curved spacetimes.

Findings

Chiral subalgebras are explicitly constructed for 2d massless scalar fields.

These subalgebras embed naturally into the full algebra of observables.

Construction of subalgebras is independent of the Cauchy surface chosen.

Abstract

In this article, which builds upon the work done in our previous paper, the chiral aspects of 2dcft on globally hyperbolic Lorentzian manifolds are developed and explored within the perturbative algebraic quantum field theory (pAQFT) framework. In the example of the massless scalar field on globally hyperbolic 2-dimensional spacetimes, we identify the subalgebras of a given theory comprising only chiral (or anti-chiral) observables. These subalgebras are constructed explicitly, with the help of structures naturally associated to a Cauchy surface, for both the classical and the quantised theory, and it is shown that they then embed naturally into the algebra of the full theory. Finally, it is demonstrated that the construction of these subalgebras is independent of the choice of Cauchy surface and that they unambiguously define a covariant theory on the spaces of null-geodesics.