I have been thinking about the definition of the notation $\cal N$ and its relation to the number of supercharges in SUSY, but still feel a little confused. In dimension 2, we usually denote, for example, $\cal N = (2,2)$ supersymmetry, where we have 2 chiral supercharge and 2 anti-chiral supercharge; but in higher dimensions we just refer to $\cal N = 1$, etc. What is the difference and why we make such different notation?

Also, I would appreciate of one can explain the exact meaning of $\cal N$, for example in 4 dimensions, and how they are related to number of supercharge $Q$ and independent spinors.

This post imported from StackExchange Physics at 2014-04-13 14:40 (UCT), posted by SE-user Kevin Ye