Wilson loops and topological phases in closed string theory

TL;DR

This paper explores topological invariants in closed string theory, linking Wilson loops to vacuum wave functionals and comparing these findings with 2D QED, revealing new insights into topological phases.

Contribution

It introduces a covariant phase space approach to topological invariants in closed string theory and connects Wilson loops to vacuum states, offering a novel perspective.

Findings

Wilson loops correspond to vacuum wave functionals with zero energy

Topological invariants are preserved under certain Wilson loops

Connections to 2D QED are discussed

Abstract

Using covariant phase space formulations for the natural topological invariants associated with the world-surface in closed string theory, we find that certain Wilson loops defined on the world-surface and that preserve topological invariance, correspond to wave functionals for the vacuum state with zero energy. The differences and similarities with the 2-dimensional QED proposed by Schwinger early are discussed.