Superconformal Field Theory In Six Dimensions And Supertwistor

Understand

We studied the quantum dynamics of six dimensional $\mathcal{N}=(2, 0)$ superconformal field theory (the QNG theory).

• We developed the spinor technique for six-dimensional quantum field theories.
• By combining this technique with the canonical quantization procedure, we can overcome the subtlety of the chiral nature of $\mathcal{N}=(2, 0)$ free tensor multiplet and work out its quantum mechanical theory.
• We then studied the $\mathbf{T}^2$ compactification of the QNG theory and argued that the resulting four dimensional quantum field theory is indeed the $\mathcal{N}=4$ super-Yang-Mills theory with the $SL(2, \mathbf{Z})$ duality coming from the mapping class symmetries of $\mathbf{T}^2$.