Gauge dual and noncommutative extension of anN=2supergravity solution

We investigate some properties of a recent supergravity solution of Pilch and Warner, which is dual to the $\mathcal{N}=4\mathrm{}$ gauge theory softly broken to $\mathcal{N}=2.\mathrm{}$ We verify that a D3-brane probe has the expected moduli space and its effective action can be brought to $\mathcal{N}=2\mathrm{}$ form. The kinetic term for the probe vanishes on an enhançon locus, as in earlier work on large-$N$ $\mathcal{N}=2\mathrm{}$ theories, though for the Pilch-Warner solution this locus is a line rather than a ring. On the gauge theory side we find that the probe metric can be obtained from a perturbative one-loop calculation; this principle may be useful in obtaining the supergravity dual at more general points in the $\mathcal{N}=2\mathrm{}$ gauge theory moduli space. We then turn on a B-field, following earlier work on the $\mathcal{N}=4\mathrm{}$ theory, to obtain the supergravity dual to the noncommutative $\mathcal{N}=2\mathrm{}$ theory.