Physics Asked by RM2401 on August 10, 2021
A vector superfield is defined by postulating an invariance under a linear transformation in the space of vector superfields:
$V longrightarrow V + iLambda – iLambda^{dagger}$
where $iLambda – iLambda^{dagger}$ is a vector superfield.
My question, however, is concerning the mass dimension of the superfields involved.
We know that the vector superfield V has a zero mass dimension, whereas the chiral superfield $Lambda$ has a mass dimension of 1 (The combination $iLambda – iLambda^{dagger}$as stated is a vector superfield.)
So how is it possible to define this supergauge transformation, where we have added a mass dimensional quantity to one which has no mass dimension?
You assume canonical mass dimensions for $V$ and $Lambda$. But you can in general choose non-canonical ones. So $Lambda$ here can have $0$ mass dimension. If you insist on it having mass dimension 1, you can compensate it by a mass parameter of your theory.
Answered by Kosm on August 10, 2021
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