Probability distributions for the stress tensor in conformal field theories

TL;DR

This paper develops new methods to derive explicit probability distributions for the smeared stress tensor in two-dimensional conformal quantum field theories, revealing a shifted Gamma distribution pattern.

Contribution

It introduces a novel approach based on conformal welding and extends existing moment generating function techniques to analyze stress tensor distributions.

Findings

Explicit distributions for the smeared stress tensor in vacuum states.

Distribution is often a shifted Gamma distribution.

Provides new insights into quantum fluctuations of the stress tensor.

Abstract

The vacuum state -- or any other state of finite energy -- is not an eigenstate of any smeared (averaged) local quantum field. The outcomes (spectral values) of repeated measurements of that averaged local quantum field are therefore distributed according to a non-trivial probability distribution. In this paper, we study probability distributions for the smeared stress tensor in two dimensional conformal quantum field theory. We first provide a new general method for this task based on the famous conformal welding problem in complex analysis. Secondly, we extend the known moment generating function method of Fewster, Ford and Roman. Our analysis provides new explicit probability distributions for the smeared stress tensor in the vacuum for various infinite classes of smearing functions. All of these turn out to be given in the end by a shifted Gamma distribution, pointing, perhaps, at a distinguished role of this distribution in the problem at hand.