Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Monopoles, Duality, and String Theory

Joseph Polchinski

TL;DR

This work argues that magnetic monopoles are a natural consequence of charge quantization and unification, supported by several frameworks including Grand Unification, Kaluza-Klein theory, lattice gauge theory, Kalb-Ramond fields, and D-branes. It posits two completeness principles—that charge quantization implies monopoles and that fully unified theories host electric and magnetic sources with the minimal Dirac unit—and illustrates them with concrete examples. The author highlights dualities that map electric and magnetic sectors onto each other and shows how string theory interlinks diverse objects, pointing to a deep, unifying structure in high-energy physics. Despite experimental challenges and cosmological dilution of monopoles, the paper argues for the theoretical inevitability and significance of monopoles within a broader, duality-rich framework.

Abstract

Dirac showed that the existence of magnetic monopoles would imply quantization of electric charge. I discuss the converse, and propose two `principles of completeness' which I illustrate with various examples.

Monopoles, Duality, and String Theory

TL;DR

This work argues that magnetic monopoles are a natural consequence of charge quantization and unification, supported by several frameworks including Grand Unification, Kaluza-Klein theory, lattice gauge theory, Kalb-Ramond fields, and D-branes. It posits two completeness principles—that charge quantization implies monopoles and that fully unified theories host electric and magnetic sources with the minimal Dirac unit—and illustrates them with concrete examples. The author highlights dualities that map electric and magnetic sectors onto each other and shows how string theory interlinks diverse objects, pointing to a deep, unifying structure in high-energy physics. Despite experimental challenges and cosmological dilution of monopoles, the paper argues for the theoretical inevitability and significance of monopoles within a broader, duality-rich framework.

Abstract

Dirac showed that the existence of magnetic monopoles would imply quantization of electric charge. I discuss the converse, and propose two `principles of completeness' which I illustrate with various examples.

Paper Structure

This paper contains 10 sections, 8 equations, 3 figures.

Table of Contents

  1. Theory
  2. The Necessity of Monopoles
  3. Grand Unification
  4. Kaluza-Klein Theory
  5. $U(1)$ Lattice Gauge Theory
  6. The Kalb-Ramond Field
  7. D-Branes
  8. Conclusions
  9. The Existence of Monopoles
  10. Duality and Beauty

Figures (3)

  • Figure 1: A Dirac string extending from the monopole.
  • Figure 2: Part of a spatial lattice. A typical link $l$ and plaquette $P$ are illustrated. A magnetic monopole and its Dirac string are shown, hidden between the sites of the lattice.
  • Figure 3: Two D-branes (the vertical planes) and a cylindrical string world-sheet with one boundary on each D-brane. The world-sheet can be regarded either as an open string with one end on each D-brane (the dotted line) traveling in a vacuum loop, or a closed string (the dashed line) emitted by one D-brane and absorbed by the other.