SLE($\kappa,\rho$)and Boundary Coulomb Gas

TL;DR

This paper explores the connection between Coulomb gas models with various boundary conditions and SLE($, ho$) theories, deriving conditions on charges and parameters, and investigates boundary operators in free fermion theories.

Contribution

It establishes a link between Coulomb gas boundary conditions and SLE($, ho$) parameters, and analyzes boundary operators in free fermion theories.

Findings

Derived conditions relating charges and SLE parameters.

Connected Coulomb gas models to SLE($, ho$) theories.

Identified logarithmic boundary operators in free fermion models.

Abstract

We consider the coulomb gas model on the upper half plane with different boundary conditions, namely Drichlet, Neuman and mixed. We related this model to SLE($\kappa,\rho$) theories. We derive a set of conditions connecting the total charge of the coulomb gas, the boundary charges, the parameters $\kappa$ and $\rho$. Also we study a free fermion theory in presence of a boundary and show with the same methods that it would lead to logarithmic boundary changing operators.