Gauge Dual and Noncommutative Extension of an N=2 Supergravity Solution

TL;DR

The authors analyze the Pilch–Warner ${ m N}=2^*$ holographic dual, confirming that a D3-brane probe reproduces the ${ m N}=2$ moduli space and that the probe action takes the expected ${ m N}=2$ form. They identify an enhançon–like locus that is a line in PW and show the gravity data matches a perturbative ${ m N}=2$ gauge theory calculation, offering guidance to extract more of the full supergravity solution from gauge theory. They then construct a noncommutative extension by turning on a constant ${B}$ field and demonstrate that the D3-brane probe moduli space is unchanged by noncommutativity, aligning with field theory expectations. This work provides a coherent link between PW flows, their noncommutative extensions, and perturbative gauge theory in a holographic framework.

Abstract

We investigate some properties of a recent supergravity solution of Pilch and Warner, which is dual to the N=4 gauge theory softly broken to N=2. We verify that a D3-brane probe has the expected moduli space and its effective action can be brought to N=2 form. The kinetic term for the probe vanishes on an enhancon locus, as in earlier work on large-n N=2 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 N=2 gauge theory moduli space. We then turn on a B-field, following earlier work on the N=4 theory, to obtain the supergravity dual to the noncommutative N=2 theory.