This is with reference to M. J. Strassler's lectures on "The Duality Cascade" pg. 46. I want to see how $\mathcal{N}=4$ SYM emerges when D3 branes, in the KW setup, are placed at smooth point of the conifold, purely from field theory point of view.

That is: Given a $U(N) \times U(N)$ quiver with $A_i$ and $B_i$ in the bi-fundamental and the anti-bi-fundamental respectively and an $SU(2) \times SU(2)$ invariant quartic superpotential (which vanishes for $N=1$), in what manner do we higgs the theory so as to get $\mathcal{N}=4$ SYM?

For the case of $N=1$ there is a comment in the lectures. It says,

... suppose we just have one D3 brane and we allow $A_1B_1$ to have an expectation value, so that the D-brane sits at some point away from the singular point of the conifold. Then the gauge group is broken to $U (1)$, and six scalars remain massless — the six possible translations of the D3-brane away from its initial point — exactly the number needed to fill out an $\mathcal{N}= 4$ $U(1)$ vector multiplet.

I want to understand this statement. Please help me understand how to work out for case of $N=1$. I can try for the generic value of $N$.


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