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Mass dimension and Abelian super-gauge transformation

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?

One Answer

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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