- I would like to know what is exactly meant when one writes θ±,ˉθ±,Q±,ˉQ±,D±,ˉD±.
{..I typically encounter this notation in literature on 2+1 dimensional SUSY like super-Chern-Simon's theory..}
- I guess that when one has only half the super-space (i.e only the + of the above or the −) it is called the (0,2) superspace compared to the usual (2,2) superspace. In this case of (0,2) SUSY I have seen the following definitions,
Q+=∂∂θ++iˉθ+(∂∂y0+∂∂y1)
ˉQ+=−∂∂ˉθ+−iθ+(∂∂y0+∂∂y1)
which commute with,
D+=∂∂θ+−iˉθ+(∂∂y0+∂∂y1)
ˉD+=−∂∂ˉθ++iθ+(∂∂y0+∂∂y1)
- I am guessing that there is an exactly corresponding partner to the above equations with + replaced by −. Right?
How does the above formalism compare to the more familiar version as,
Qα=∂∂θα−iσμα˙αˉθ˙α∂∂xμ
ˉQ˙α=−∂∂ˉθ˙α+iσμα˙αθα∂∂xμ
which commute with,
Dα=∂∂θα+iσμα˙αˉθ˙α∂∂xμ
ˉD˙α=−∂∂ˉθ˙α−iσμα˙αθα∂∂xμ
{..compared to the above conventional setting, in the ± notation among many things the most perplexing is the absence of the Pauli matrices!..why?..}
I would be very grateful if someone can explain this notation.
{..often it turns out that not just the Qs and the Ds but also various superfields also acquaire a ± subscript and various usual factors of Pauli matrices look missing..it would be great if someone can help clarify this..}
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