An N=1 Supersymmetric Coulomb Flow

We find a three-parameter family of solutions to IIB supergravity that corresponds to N=1 supersymmetric holographic RG flows of N=4 supersymmetric Yang Mills theory. This family of solutions allows one to give a mass to a single chiral superfield, and to probe a two-dimensional subspace of the Coulomb branch. In particular, we examine part of the Coulomb branch of the Leigh-Strassler fixed point. We look at the infra-red asymptotics of these flows from the ten-dimensional perspective. We also make general conjectures for the lifting Ansatz of five-dimensional scalar configurations to ten-dimensional tensor gauge fields. Our solution provides a highly non-trivial test of these conjectures.Comment: 13 pages; harvma

A Class of N=1 Supersymmetric RG Flows from Five-dimensional N = 8 Supergravity

We consider the holographic dual of a general class of N=1* flows in which all three chiral multiplets have independent masses, and in which the corresponding Yang-Mills scalars can develop particular supersymmetry-preserving vevs. We also allow the gaugino to develop a vev. This leads to a six parameter subspace of the supergravity scalar action, and we show that this is a consistent truncation, and obtain a superpotential that governs the N=1* flows on this subspace. We analyse some of the structure of the superpotential, and check consistency with the asymptotic behaviour near the UV fixed point. We show that the dimensions of the six couplings obey a sum rule all along the N=1* flows. We also show how our superpotential describes part of the Coulomb branch of the non-trivial N=1 fixed point theory.Comment: 14 pages; harvmac. New version has only minor correction

New Vacua of Gauged N=8 Supergravity

We analyze a particular SU(2) invariant sector of the scalar manifold of gauged N=8 supergravity in five dimensions, and find all the critical points of the potential within this sector. The critical points give rise to Anti-de Sitter vacua, and preserve at least an SU(2) gauge symmetry. Consistent truncation implies that these solutions correspond to Anti-de Sitter compactifications of IIB supergravity, and hence to possible near-horizon geometries of 3-branes. Thus we find new conformal phases of softly broken N=4 Yang--Mills theory. One of the critical points preserves N=2 supersymmetry in the bulk and is therefore completely stable, and corresponds to an N=1 superconformal fixed point of the Yang--Mills theory. The corresponding renormalization group flow from the N=4 point has c_{IR}/c_{UV} = 27/32. We also discuss the ten-dimensional geometries corresponding to these critical points.Comment: 14 pages, 1 table, harvma

An N = 2 Supersymmetric Membrane Flow

We find M-theory solutions that are holographic duals of flows of the maximally supersymmetric N=8 scalar-fermion theory in (2+1) dimensions. In particular, we construct the M-theory solution dual to a flow in which a single chiral multiplet is given a mass, and the theory goes to a new infra-red fixed point. We also examine this new solution using M2-brane probes. The (2+1)-dimensional field theory fixed-point is closely related to that of Leigh and Strassler, while the M-theory solution is closely related to the corresponding IIB flow solution. We recast the IIB flow solution in a more geometric manner and use this to obtain an Ansatz for the M-theory flow. We are able to generalize our solution further to obtain flows with del Pezzo sub-manifolds, and we give an explicit solution with a conifold singularity.Comment: 28 pages; harvma

Supersymmetric Charged Clouds in AdS_5

We consider supersymmetric holographic flows that involve background gauge fields dual to chemical potentials in the boundary field theory. We use a consistent truncation of gauged N=8 supergravity in five dimensions and we give a complete analysis of the supersymmetry conditions for a large family of flows. We examine how the well-known supersymmetric flow between two fixed points is modified by the presence of the chemical potentials and this yields a new, completely smooth, solution that interpolates between two global AdS spaces of different radii and with different values of the chemical potential. We also examine some black-hole-like singular flows and a new non-supersymmetric black hole solution. We comment on the interpretation of our new solutions in terms of giant gravitons and discuss the implications of our work for finding black-hole solutions in AdS geometries.Comment: 31 pages, 6 figures; minor corrections, updated reference

Consistent SO(6) Reduction Of Type IIB Supergravity on S^5

Type IIB supergravity can be consistently truncated to the metric and the self-dual 5-form. We obtain the complete non-linear Kaluza-Klein S^5 reduction Ansatz for this theory, giving rise to gravity coupled to the fifteen Yang-Mills gauge fields of SO(6) and the twenty scalars of the coset SL(6,R)/SO(6). This provides a consistent embedding of this subsector of N=8, D=5 gauged supergravity in type IIB in D=10. We demonstrate that the self-duality of the 5-form plays a crucial role in the consistency of the reduction. We also discuss certain necessary conditions for a theory of gravity and an antisymmetric tensor in an arbitrary dimension D to admit a consistent sphere reduction, keeping all the massless fields. We find that it is only possible for D=11, with a 4-form field, and D=10, with a 5-form. Furthermore, in D=11 the full bosonic structure of eleven-dimensional supergravity is required, while in D=10 the 5-form must be self-dual. It is remarkable that just from the consistency requirement alone one would discover D=11 and type IIB supergravities, and that D=11 is an upper bound on the dimension.Comment: Latex, 14 pages, typos corrected and comments adde

Geometry of The Embedding of Supergravity Scalar Manifolds in D=11 and D=10

Several recent papers have made considerable progress in proving the existence of remarkable consistent Kaluza-Klein sphere reductions of D=10 and D=11 supergravities, to give gauged supergravities in lower dimensions. A proof of the consistency of the full gauged SO(8) reduction on S^7 from D=11 was given many years ago, but from a practical viewpoint a reduction to a smaller subset of the fields can be more manageable, for the purposes of lifting lower-dimensional solutions back to the higher dimension. The major complexity of the spherical reduction Ansatze comes from the spin-0 fields, and of these, it is the pseudoscalars that are the most difficult to handle. In this paper we address this problem in two cases. One arises in a truncation of SO(8) gauged supergravity in four dimensions to U(1)^4, where there are three pairs of dilatons and axions in the scalar sector. The other example involves the truncation of SO(6) gauged supergravity in D=5 to a subsector containing a scalar and a pseudoscalar field, with a potential that admits a second supersymmetric vacuum aside from the maximally-supersymmetric one. We briefly discuss the use of these emdedding Ansatze for the lifting of solutions back to the higher dimension.Comment: Latex, 24 pages, typos correcte

Hidden symmetries in minimal five-dimensional supergravity

We study the hidden symmetries arising in the dimensional reduction of d=5, N=2 supergravity to three dimensions. Extending previous partial results for the bosonic part, we give a derivation that includes fermionic terms, shedding light on the appearance of the local hidden symmetry SO(4) in the reduction.Comment: 11 pages LaTeX, uses elsart and amssym

Consistent truncation of d = 11 supergravity on AdS_4 x S^7

We study the system of equations derived twenty five years ago by B. de Wit and the first author [Nucl. Phys. B281 (1987) 211] as conditions for the consistent truncation of eleven-dimensional supergravity on AdS_4 x S^7 to gauged N = 8 supergravity in four dimensions. By exploiting the E_7(7) symmetry, we determine the most general solution to this system at each point on the coset space E_7(7)/SU(8). We show that invariants of the general solution are given by the fluxes in eleven-dimensional supergravity. This allows us to both clarify the explicit non-linear ansatze for the fluxes given previously and to fill a gap in the original proof of the consistent truncation. These results are illustrated with several examples.Comment: 41 pages, typos corrected, published versio

Orbifolds and Flows from Gauged Supergravity

We examine orbifolds of the IIB string via gauged supergravity. For the gravity duals of the A_{n-1} quiver gauge theories, we extract the massless degrees of freedom and assemble them into multiplets of N=4 gauged supergravity in five dimensions. We examine the embedding of the gauge group into the isometry group of the scalar manifold, as well as the symmetries of the scalar potential. From this we find that there is a large SU(1,n) symmetry group which relates different RG flows in the dual quiver gauge theory. We find that this symmetry implies an extension of the usual duality between ten-dimensional IIB solutions which involves exchanging geometric moduli with background fluxes.Comment: 37 pages, harvma