Harmonic Superspace

October 26 - November 2

Institut Henri Poincare

Emery Sokatchev (Annecy)

COMING SOON

Part 1 HARMONIC SUPERSPACE

• Coset spaces for the Poincaré and super Poincaré groups

• N=2 harmonic superspace

• Harmonic variables

• Harmonic covariant derivatives

• Reality properties

• Harmonic expansion on the 2-sphere

• Harmonic integrals

• Differential equations on the 2-sphere

• Harmonic distributions

Part 2 N=2 MATTER WITH INFINITE AND FINITE SETS OF AUXILIARY FIELDS

• N=2 matter multiplets on shell; why do we need infinitely many auxiliary fields?

• Free off-shell hypermultiplet and Grassmann analyticity

• Hypermultiplet self-couplings. General action for hypermultiplets. Example of the Taub-NUT sigma model

• N=2 matter multiplets with a finite number of auxiliary fields. N=2 duality transformations

Part 3 SUPERSYMMETRIC YANG-MILLS THEORY

• Gauge (super)fields from matter couplings

• Superspace differential geometry

• N=2 SYM action

Part 4 HARMONICS SUPERGRAPHS

• Green's functions for hypermultiplets

• N=2 SYM: gauge fixing, Green's functions and ghosts

• Feynman rules

• Examples of supergraph calculations

Part 5 N=3 SUPERSYMMETRIC YANG-MILLS THEORY

• N=3 SYM on-shell constraints

• N=3 harmonic variables, Grassmann analyticity and the interpretation of the N=3 SYM constraints

• Off-shell Chern-Simons-type action