# Vacuum expectation value of twist fields

## TL;DR

This paper investigates the vacuum expectation values of twist fields using a path integral approach, reducing the problem to matter fields in Aharonov-Bohm vortices and deriving formulas via zeta function regularization.

## Contribution

It introduces a novel method to compute twist field VEVs by connecting them to functional determinants in external vortex backgrounds.

## Key findings

- Derived concise formulas for twist field VEVs.
- Connected twist field correlators to Bessel zero spectra.
- Provided a regularization framework for these determinants.

## Abstract

Twist fields emerge in a number of physical applications ranging from entanglement entropy to scattering amplitudes in four-dimensional gauge theories. In this work, their vacuum expectation values are studied in the path integral framework. By performing a gauge transformation, their correlation functions are reduced to field theory of matter fields in external Aharonov-Bohm vortices. The resulting functional determinants are then analyzed within the zeta function regularization for the spectrum of Bessel zeros and concise formulas are derived.