Field Theory Operator Encoding in N=2 Geometries

TL;DR

This paper explores supergravity solutions dual to N=2 super Yang-Mills theory, identifying the moduli space and scalar operators, and providing a consistency check for the gauge/gravity duality through D5 brane distributions.

Contribution

It introduces a coordinate system where the field theory's N=2 structure is explicit and relates the geometry to the running coupling and scalar operators, validating the duality.

Findings

The geometry simplifies to two key functions on the moduli space.

D5 brane distributions match the expected scalar operators.

The approach provides the first non-trivial consistency check of the duality.

Abstract

We investigate supergravity solutions describing D5 branes wrapped on a two cycle which are dual to N=2 super Yang Mills theory. Brane probing these solutions allows the moduli space of the field theory to be identified. There are a unique set of coordinates in which the field theory on the probe takes an N=2 form and in these coordinates the running coupling of the gauge theory may be identified. We show that the geometry, when restricted to the moduli space, takes a very simple form involving only two functions. One is the running gauge coupling whilst the other parametrizes the scalar operators of the field theory. The D5 brane distributions, for the full set of solutions in the literature,can be determined by assuming the field theory's form for the running coupling as a function of scalar vevs. We show that the resulting distributions also correctly reproduce the scalar operators parametrized elsewhere providing the first non-trivial consistency check on the duality.