Towards integrable perturbation of 2d CFT on de Sitter space

TL;DR

This paper proposes a method to deform 2D conformal field theories to potentially create models on de Sitter space by adding primary fields to the conformal net's generators, demonstrated with a U(1)-current extension.

Contribution

It introduces a novel deformation procedure for 2D conformal nets to construct models on de Sitter space, including explicit examples with charged fields.

Findings

Perturbing operators are well-defined on a dense domain.

The deformation preserves certain algebraic structures.

Example with U(1)-current net extended by a charged field.

Abstract

We describe a procedure to deform the dynamics of a two-dimensional conformal net to possibly obtain a Haag-Kastler net on the de Sitter spacetime. The new dynamics is given by adding a primary field smeared on the time-zero circle to the Lorentz generators of the conformal net. As an example, we take an extension of the chiral U(1)-current net by a charged field with conformal dimension d < 1/4. We show that the perturbing operators are defined on a dense domain.