Electromagnetic duality for children
In the Fall and Winter terms 1995-6, I gave a series of ten
lectures on electromagnetic duality to members of the QMW
String Theory group. The lectures started from very basic
material and ended with Sen's test of the predicted dyonic
spectrum at monopole number 2 for the gauge group SU(2).
The full set of
lectures has not changed since late 1998. The tenth and
last lecture has still to be typed. However there is a new
section on the extension to arbitrary compact simple gauge
The notes include about 150 exercises of varying difficulty,
but the solutions have yet to be typed.
Dirac monopole, dyons, Dirac-Schwinger-Zwanziger
quantisation condition. The 't Hooft-Polyakov monopole.
Magnetic charge as topology. Prasad-Sommerfield limit,
Bogomol'nyi bound. The Montonen-Olive conjecture.
The Witten effect and SL(2,ℤ) duality.
Supersymmetry, central charges and the Bogomol'nyi bound
revisited: short multiplets.
N=2 supersymmetric Yang-Mills: BPS states revisited.
Monopole moduli space, collective coordinates, low energy
dynamics. Dyonic spectrum for 1-monopole sector.
Moduli space of N=2 supersymmetric BPS monopoles, low energy
dynamics. Bound states.
"Forget it all for an instanton!"
Details of the calculation of the number of collective
coordinates: an example of an index theorem calculation
for operators on open spaces.
N=4 supersymmetric Yang-Mills from 10 dimensions -- yet
another avatar of the BPS monopole.
Effective action for N=4 supersymmetric Yang-Mills. The
Atiyah-Hitchin metric on the 2-monopole moduli space. Sen's
The original aim of the lectures was to study the
Seiberg-Witten solution of N=2 supersymmetric gauge theories,
and the working title was On the road to
Seiberg-Witten. The road instead detoured towards the
self-duality of N=4 supersymmetric Yang-Mills theory in four
© José Figueroa-O'Farrill