Lagrange multiplier in Plebanski action

Hi,
I am studying a little bit of loop quantum gravity these days. And I
am a little bit confused.
EInstein-Hilbert action can be written as Sigma^F + lambda Sigma
^Sigma + Psi Sigma^Sigma.
Where the first term is curvature and the second term cosmological
constant and the third term Lagrange multiplier.
What is this Lagrange multiplier?
I know Lagrange multiplier from my multivariable calculus class, but
do not really understand what this Lagrange multiplier is in this
Lagrangian action. Is this something like gauge fixing term?
One thing that I don't understand is that my other book seems to
ignore this last term and just write out this action as SIgma^F +
lambda Sigma^Sigma.
However, another paper(hep-th/0411073) points out that if the action
is written without this Lagrange multiplier, this action corresponds
to anti self-dual Einstein manifold which is rather peculiar.
Could somebody explain this in detail to me?

Youngsub

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