is the 't Hooft symbol:
-
Where and are instances of the Kronecker delta, and is the Levi-Civita symbol.
In other words, they are defined by
( )
-
-
where the latter are the anti-self-dual 't Hooft symbols.
In matrix form, the 't Hooft symbols are
-
and their anti-self-duals are the following:
-
They satisfy the self-duality and the anti-self-duality properties:
-
Some other properties are
-
-
-
-
-
The same holds for except for
-
and
-
Obviously due to different
duality properties.
Many properties of these are tabulated in the appendix of 't Hooft's paper[1] and also in the article by Belitsky et al.[2]