Duality (electric–magnetic)

Duality (electric–magnetic)
Name	Duality (electric–magnetic)
Field	Electromagnetism, Quantum Field Theory, String Theory
Introduced	19th century
Notable	James Clerk Maxwell, Paul Dirac, Edward Witten

Contents

Duality (electric–magnetic) Duality (electric–magnetic) is the symmetry relating electric and magnetic fields and charges that appears across James Clerk Maxwell, Paul Dirac, Julian Schwinger, Edward Witten, Niels Bohr and Michael Faraday-inspired frameworks. It connects concepts from Maxwell's equations, quantum electrodynamics, non-Abelian gauge theory, string theory, topology and quantum field theory while guiding searches by institutions such as CERN, Fermilab, SLAC National Accelerator Laboratory and observatories like Hubble Space Telescope and Event Horizon Telescope.

Introduction

In vacuum Maxwellian duality interchanges the homogeneous and inhomogeneous Maxwell equations and mixes electric field and magnetic field components in solutions related to James Clerk Maxwell, Oliver Heaviside, Hermann von Helmholtz and Ludwig Lorenz; historically this symmetry was explored in debates involving Michael Faraday, Lord Kelvin and William Rowan Hamilton. Classical formulations influenced electromagnetic engineering at Bell Labs, General Electric, Siemens and informed experiments by Heinrich Hertz, Nikola Tesla, Guglielmo Marconi and Samuel Morse, while mathematical treatments drew on work by Carl Friedrich Gauss, Siméon Denis Poisson and Augustin-Jean Fresnel.

Quantum extensions developed within quantum electrodynamics (QED) by Paul Dirac, Richard Feynman, Sin-Itiro Tomonaga, Julian Schwinger and Freeman Dyson introduced the concept of magnetic monopoles and charge quantization, producing the Dirac quantization condition that links electric charge and hypothetical magnetic charge. Dirac's argument influenced later theoretical studies by Gerard 't Hooft, Alexander Polyakov, Edward Witten, Nathan Seiberg and Ashoke Sen, and experimental programs at Brookhaven National Laboratory, Rutherford Appleton Laboratory and Los Alamos National Laboratory have searched for monopoles predicted in grand unified scenarios advocated by Sheldon Glashow, Howard Georgi and Peter Higgs.

S-duality relates strong and weak coupling regimes in non-Abelian gauge theory and was developed in contexts involving Montonen–Olive conjecture, N=4 supersymmetry, Seiberg–Witten theory and contributions by Nathan Seiberg, Edward Witten, Cumrun Vafa, Ashoke Sen and Gerard 't Hooft. It underpins dual descriptions in supersymmetric Yang–Mills theory, links to modular transformations studied by Srinivasa Ramanujan, Goro Shimura and John Conway, and shaped research programs at Princeton University, Institute for Advanced Study, CERN and Perimeter Institute.

In string theory, electric–magnetic dualities manifest as T-duality, S-duality and U-duality connecting different string backgrounds, brane configurations and compactifications studied by Joseph Polchinski, Edward Witten, Juan Maldacena, Ashoke Sen and Cumrun Vafa. These dualities relate Type IIB string theory, M-theory, heterotic string and Type IIA string formulations and play central roles in the AdS/CFT correspondence developed by Juan Maldacena, influencing research at Institute for Advanced Study, Caltech, Stanford University and Kavli Institute for Theoretical Physics.

Mathematically, electric–magnetic duality invokes differential forms, Hodge duality, cohomology, fiber bundles and characteristic classes derived in work by Élie Cartan, Hermann Weyl, André Weil, Alexander Grothendieck, Michael Atiyah and Isadore Singer. Topological solitons, monopoles and instantons connect to Donaldson theory, Seiberg–Witten invariants, Chern–Simons theory and constructions by Simon Donaldson, Edward Witten, Maxwell equations-linked analyses and institutions such as Institute for Advanced Study and Mathematical Sciences Research Institute.

Searches for magnetic monopoles and electric–magnetic asymmetries have been conducted in cosmic ray experiments at Pierre Auger Observatory, IceCube Neutrino Observatory, Super-Kamiokande, MACRO experiment and collider experiments at Large Hadron Collider, ATLAS experiment, CMS experiment and Tevatron; astrophysical constraints derive from observations by Planck satellite, Fermi Gamma-ray Space Telescope, Hubble Space Telescope and Event Horizon Telescope. Null results constrain monopole masses and couplings in models proposed by Sheldon Glashow, Howard Georgi, Paul Dirac and Georgi–Glashow model while proposals for detection involve technologies developed at Brookhaven National Laboratory, SLAC National Accelerator Laboratory, CERN and national laboratories in Japan, Germany and United States.