Dynamical Description of Spectral Flow in N=2 Superconformal Field Theories

TL;DR

This paper presents a three-dimensional dynamical framework using Chern-Simons gauge theory to describe spectral flow in N=2 superconformal field theories, linking boundary conditions and GSO-projection.

Contribution

It introduces a novel three-dimensional description of spectral flow via charged particle propagation in Chern-Simons theory, providing a dynamic understanding of boundary condition transitions.

Findings

Spectral flow can be modeled as particle propagation in Chern-Simons theory.

Quantum mixing of Chern-Simons vacua explains boundary condition changes.

Provides a dynamical picture for the GSO-projection in superconformal theories.

Abstract

We show how the spectral flow between the Neveu-Schwarz and Ramond sectors of N=2 superconformal field theories can be described in three dimensions in terms of the propagation of charged particles coupled to a a Chern-Simons gauge theory. Quantum mechanical mixing between the degenerate Chern-Simons vacua interpolates between the different boundary conditions of the two sectors and so provides a dynamical picture for the GSO-projection.