Correlation functions of disorder operators in massive ghost theories

TL;DR

This paper analyzes the correlation functions of disorder operators in massive ghost theories, revealing their dependence on statistics and providing exact expressions through nonlinear differential equations.

Contribution

It provides a unified framework for computing correlation functions of disorder operators in ghost and ordinary field theories, highlighting their dependence on statistics.

Findings

Correlation functions depend only on statistics.

Correlation functions are inverse for bosonic and fermionic cases.

Exact solutions are obtained via nonlinear differential equations.

Abstract

The two-dimensional ghost systems with negative integral central charge received much attention in the last years for their role in a number of applications and in connection with logarithmic conformal field theory. We consider the free massive bosonic and fermionic ghost systems and concentrate on the non-trivial sectors containing the disorder operators. A unified analysis of the correlation functions of such operators can be performed for ghosts and ordinary complex bosons and fermions. It turns out that these correlators depend only on the statistics although the scaling dimensions of the disorder operators change when going from the ordinary to the ghost case. As known from the study of the ordinary case, the bosonic and fermionic correlation functions are the inverse of each other and are exactly expressible through the solution of a non-linear differential equation.