# Supersymmetric basic question

1. Dec 30, 2011

### Neitrino

HI,

We can construct vector superfield by chiral field minus anti chiral super field (example Bailin-Love page 59 expression 3.23)

So does this vector superfield have a kinetic term-WW ? since the for the kinetic term we have expression 3.37 and it seems that if vector superfield is defined as in 3.23 then all terms in kinetic expression are zero.

Thank you

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2. Dec 30, 2011

### fzero

$V_{\mu\nu}$ in 3.37 is the field strength tensor for the Lorentz vector field $V_{\mu}$ appearing as the lowest component of $V_{WZ}$ in 3.23. There are no extra $\theta$s appearing in the terms in 3.37. In the abelian theory considered there,

$V_{\mu\nu} = \partial_\mu V_\nu - \partial_\nu V_\mu.$

I think that your confusion is due to the fact that the authors are using $V$ to represent at least 3 different but related objects.

3. Dec 31, 2011

### suprised

The confusion is that this is not a vector superfield with a propagating spin-1 component, rather the gauge field component is pure gauge. The point is that the combination "chiral field minus anti chiral super field" is precisely how a local gauge transformation acts on a vector superfield, so this is precisely the superspace generalization of writing

variation(A_mu) = del_mu phi

which does not describe a physical degree of freedom.

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