# Spectral determinants for twist field correlators

## TL;DR

This paper analyzes two-point correlation functions of twist fields in a free massless scalar theory, using spectral determinants and zeta function regularization, revealing non-trivial properties and extending insights to massive scalars.

## Contribution

It provides an exact computation of twist field correlators via spectral determinants and introduces a novel approach for massive scalars using the Lifshitz-Krein trace formula.

## Key findings

- Exact spectral determinant calculations for twist correlators.
- Non-trivial properties of twist-anti-twist correlators in free scalar theory.
- Extension of methods to massive complex scalars.

## Abstract

Twist fields were introduced a few decades ago as a quantum counterpart to classical kink configurations and disorder variables in low dimensional field theories. In recent years they received a new incarnation within the framework of geometric entropy and strong coupling limit of four-dimensional scattering amplitudes. In this paper, we study their two-point correlation functions in a free massless scalar theory, namely, twist--twist and twist--anti-twist correlators. In spite of the simplicity of the model in question, the properties of the latter are far from being trivial. The problem is reduced, within the formalism of the path integral, to the study of spectral determinants on surfaces with conical points, which are then computed exactly making use of the zeta function regularization. We also provide an insight into twist correlators for a massive complex scalar by means of the Lifshitz-Krein trace formula.