# Dynamics of the Fermion-Rotor System

## TL;DR

This paper investigates the fermion-rotor system in 1+1 dimensions, revealing how the rotor influences quantum numbers and scattering, and connecting it to boundary states and anomalies in chiral theories.

## Contribution

It introduces a detailed analysis of the fermion-rotor system, showing how the rotor acts as a twist operator and exploring its role in boundary states and anomalies.

## Key findings

- The rotor acts as a twist operator changing quantum numbers.
- Fermions dressed with the rotor create single-particle states.
- Identifies a mod 2 anomaly related to the Witten anomaly.

## Abstract

We explore the dynamics of the fermion-rotor system, a simple impurity model in d=1+1 dimensions that consists of a collection of purely right-moving fermions interacting with a quantum mechanical rotor localised at the origin. This was first introduced by Polchinski as a toy model for monopole-fermion scattering and is surprisingly subtle, with ingoing and outgoing fermions carrying different quantum numbers. We show that the rotor acts as a twist operator in the low-energy theory, changing the quantum numbers of excitations that have previously passed through the origin to ensure scattering consistent with all symmetries. We further show how generalisations of this model with multiple rotors and unequal charges can be viewed as a UV-completion of boundary states for chiral theories, including the well-studied 3450 model. We compute correlation functions between ingoing and outgoing fermions and show that fermions dressed with the rotor degree of freedom act as local operators and create single-particle states, generalising an earlier result obtained in a theory with a single rotor and equal charges. Finally, we point out a mod 2 anomaly in these models that descends from the Witten anomaly in 4d