# Schramm's formula and the Green's function for multiple SLE

## TL;DR

This paper develops explicit formulas for the Green's function and Schramm's formula for multiple SLEs using CFT techniques, extending previous results to systems of multiple curves and confirming some physics predictions.

## Contribution

It introduces a method to construct martingale observables for multiple SLEs via screening in CFT, providing rigorous proofs of formulas previously predicted in physics literature.

## Key findings

- Explicit Green's function for two SLE curves
- Schramm's formula for multiple SLEs
- Validation of physics-predicted formulas in special cases

## Abstract

We construct martingale observables for systems of multiple SLE curves by applying screening techniques within the CFT framework recently developed by Kang and Makarov, extended to admit multiple SLEs. We illustrate this approach by rigorously establishing explicit expressions for the Green's function and Schramm's formula in the case of two curves growing towards infinity. In the special case when the curves are `fused' and start at the same point, some of the formulas we prove were predicted in the physics literature.