Electromagnetic duality for children
In the Fall and Winter terms 19956, 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
groups.
The notes include about 150 exercises of varying difficulty,
but the solutions have yet to be typed.
Lectures

Dirac monopole, dyons, DiracSchwingerZwanziger
quantisation condition. The 't HooftPolyakov monopole.

Magnetic charge as topology. PrasadSommerfield limit,
Bogomol'nyi bound. The MontonenOlive conjecture.

The Witten effect and SL(2,ℤ) duality.

Supersymmetry, central charges and the Bogomol'nyi bound
revisited: short multiplets.

N=2 supersymmetric YangMills: BPS states revisited.

Monopole moduli space, collective coordinates, low energy
dynamics. Dyonic spectrum for 1monopole 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 YangMills from 10 dimensions  yet
another avatar of the BPS monopole.

Effective action for N=4 supersymmetric YangMills. The
AtiyahHitchin metric on the 2monopole moduli space. Sen's
calculation.
The original aim of the lectures was to study the
SeibergWitten solution of N=2 supersymmetric gauge theories,
and the working title was On the road to
SeibergWitten. The road instead detoured towards the
selfduality of N=4 supersymmetric YangMills theory in four
dimensions.
© JosÃ© FigueroaO'Farrill