5 research outputs found
The Kahler Structure of Supersymmetric Holographic RG Flows
We study the metrics on the families of moduli spaces arising from probing
with a brane the ten and eleven dimensional supergravity solutions
corresponding to renormalisation group flows of supersymmetric large n gauge
theory. In comparing the geometry to the physics of the dual gauge theory, it
is important to identify appropriate coordinates, and starting with the case of
SU(n) gauge theories flowing from N=4 to N=1 via a mass term, we demonstrate
that the metric is Kahler, and solve for the Kahler potential everywhere along
the flow. We show that the asymptotic form of the Kahler potential, and hence
the peculiar conical form of the metric, follows from special properties of the
gauge theory. Furthermore, we find the analogous Kahler structure for the N=4
preserving Coulomb branch flows, and for an N=2 flow. In addition, we establish
similar properties for two eleven dimensional flow geometries recently
presented in the literature, one of which has a deformation of the conifold as
its moduli space. In all of these cases, we notice that the Kahler potential
appears to satisfy a simple universal differential equation. We prove that this
equation arises for all purely Coulomb branch flows dual to both ten and eleven
dimensional geometries, and conjecture that the equation holds much more
generally.Comment: 26 pages. Late
Penrose Limits, Deformed pp-Waves and the String Duals of N=1 Large n Gauge Theory
A certain conformally invariant N=1 supersymmetric SU(n) gauge theory has a
description as an infra-red fixed point obtained by deforming the N=4
supersymmetric Yang-Mills theory by giving a mass to one of its N=1 chiral
multiplets. We study the Penrose limit of the supergravity dual of the large n
limit of this N=1 gauge theory. The limit gives a pp-wave with R-R five-form
flux and both R-R and NS-NS three-form flux. We discover that this new solution
preserves twenty supercharges and that, in the light-cone gauge, string theory
on this background is exactly solvable. Correspondingly, this latter is the
stringy dual of a particular large charge limit of the large n gauge theory. We
are able to identify which operators in the field theory survive the limit to
form the string's ground state and some of the spacetime excitations. The full
string model, which we exhibit, contains a family of non-trivial predictions
for the properties of the gauge theory operators which survive the limit.Comment: 39 pages, Late