Correlation Functions of Dense Polymers and c=-2 Conformal Field Theory

TL;DR

This paper explores the correlation functions of dense lattice polymers within the framework of non-unitary c=-2 conformal field theory, revealing how zero modes are suppressed and how boundary conditions influence correlation functions.

Contribution

It demonstrates the calculation of correlation functions in the dense polymer model using non-unitary CFT and introduces the role of zero mode suppression via twist and Dirichlet operators.

Findings

Correlation functions are given by the generalized Kirchhoff theorem.

Zero modes are suppressed by twist and Dirichlet operators.

Boundary conditions are crucial for non-zero correlation functions.

Abstract

The model of dense lattice polymers is studied as an example of non-unitary Conformal Field Theory (CFT) with $c=-2$. ``Antisymmetric'' correlation functions of the model are proved to be given by the generalized Kirchhoff theorem. Continuous limit of the model is described by the free complex Grassmann field with null vacuum vector. The fundamental property of the Grassmann field and its twist field (both having non-positive conformal weights) is that they themselves suppress zero mode so that their correlation functions become non-trivial. The correlation functions of the fields with positive conformal weights are non-zero only in the presence of the Dirichlet operator that suppresses zero mode and imposes proper boundary conditions.