1,486 research outputs found
Isometry group of Sasaki-Einstein metric
We prove that the identity component of the holomorphic isometry group of a
Sasaki-Einstein metric is the identity component of a maximal compact subgroup
of its automorphism group
New Einstein-Sasaki Spaces in Five and Higher Dimensions
We obtain infinite classes of new Einstein-Sasaki metrics on complete and
non-singular manifolds. They arise, after Euclideanisation, from BPS limits of
the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces
L^{p,q,r} in five dimensions have cohomogeneity 2, and U(1) x U(1) x U(1)
isometry group. They are topologically S^2 x S^3. Their AdS/CFT duals will
describe quiver theories on the four-dimensional boundary of AdS_5. We also
obtain new Einstein-Sasaki spaces of cohomogeneity n in all odd dimensions
D=2n+1 \ge 5, with U(1)^{n+1} isometry.Comment: Revtex, 4 pages, metric regularity conditions are further refine
Marginal Deformations with U(1)^3 Global Symmetry
We generate new 11-dimensional supergravity solutions from deformations based
on U(1)^3 symmetries. The initial geometries are of the form AdS_4 x Y_7, where
Y_7 is a 7-dimensional Sasaki-Einstein space. We consider a general family of
cohomogeneity one Sasaki-Einstein spaces, as well as the recently-constructed
cohomogeneity three L^{p,q,r,s} spaces. For certain cases, such as when the
Sasaki-Einstein space is S^7, Q^{1,1,1} or M^{1,1,1}, the deformed gravity
solutions correspond to a marginal deformation of a known dual gauge theory.Comment: 28pp; Refs. added and to appear in JHE
Marginal Deformations of Field Theories with AdS_4 Duals
We generate new AdS_4 solutions of D=11 supergravity starting from AdS_4 x
X_7 solutions where X_7 has U(1)^3 isometry. We consider examples where X_7 is
weak G_2, Sasaki-Einstein or tri-Sasakian, corresponding to d=3 SCFTs with
N=1,2 or 3 supersymmetry, respectively, and where the deformed solutions
preserve N=1,2 or 1 supersymmetry, respectively. For the special cases when X_7
is M(3,2), Q(1,1,1) or N(1,1)_I we identify the exactly marginal deformation in
the dual field theory. We also show that the volume of supersymmetric 5-cycles
of N(1,1)_I agrees with the conformal dimension predicted by the baryons of the
dual field theory.Comment: 28 pages, 2 figures; v2. typos correcte
Toric Geometry, Sasaki-Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
Recently an infinite family of explicit Sasaki-Einstein metrics Y^{p,q} on
S^2 x S^3 has been discovered, where p and q are two coprime positive integers,
with q<p. These give rise to a corresponding family of Calabi-Yau cones, which
moreover are toric. Aided by several recent results in toric geometry, we show
that these are Kahler quotients C^4//U(1), namely the vacua of gauged linear
sigma models with charges (p,p,-p+q,-p-q), thereby generalising the conifold,
which is p=1,q=0. We present the corresponding toric diagrams and show that
these may be embedded in the toric diagram for the orbifold C^3/Z_{p+1}xZ_{p+1}
for all q<p with fixed p. We hence find that the Y^{p,q} manifolds are AdS/CFT
dual to an infinite class of N=1 superconformal field theories arising as IR
fixed points of toric quiver gauge theories with gauge group SU(N)^{2p}. As a
non-trivial example, we show that Y^{2,1} is an explicit irregular
Sasaki-Einstein metric on the horizon of the complex cone over the first del
Pezzo surface. The dual quiver gauge theory has already been constructed for
this case and hence we can predict the exact central charge of this theory at
its IR fixed point using the AdS/CFT correspondence. The value we obtain is a
quadratic irrational number and, remarkably, agrees with a recent purely field
theoretic calculation using a-maximisation.Comment: 54 pages, 5 figures; minor changes; further minor changes, ref [8]
added - published version; eqns 1.3, 1.4 remove
Triangle Anomalies from Einstein Manifolds
The triangle anomalies in conformal field theory, which can be used to
determine the central charge a, correspond to the Chern-Simons couplings of
gauge fields in AdS under the gauge/gravity correspondence. We present a simple
geometrical formula for the Chern-Simons couplings in the case of type IIB
supergravity compactified on a five-dimensional Einstein manifold X. When X is
a circle bundle over del Pezzo surfaces or a toric Sasaki-Einstein manifold, we
show that the gravity result is in perfect agreement with the corresponding
quiver gauge theory. Our analysis reveals an interesting connection with the
condensation of giant gravitons or dibaryon operators which effectively induces
a rolling among Sasaki-Einstein vacua.Comment: 30 pages, 5 figures; published versio
Sasaki-Einstein Manifolds
This article is an overview of some of the remarkable progress that has been
made in Sasaki-Einstein geometry over the last decade, which includes a number
of new methods of constructing Sasaki-Einstein manifolds and obstructions.Comment: 58 pages. Invited contribution to Surveys in Differential Geometry.
v2: references and discussion adde
Supersymmetric IIB Solutions with Schr\"{o}dinger Symmetry
We find a class of non-relativistic supersymmetric solutions of IIB
supergravity with non-trivial B-field that have dynamical exponent n=2 and are
invariant under the Schrodinger group. For a general Sasaki-Einstein internal
manifold with U(1)^3 isometry, the solutions have two real supercharges. When
the internal manifold is S^5, the number of supercharges can be four. We also
find a large class of non-relativistic scale invariant type IIB solutions with
dynamical exponents different from two. The explicit solutions and the values
of the dynamical exponents are determined by vector eigenfunctions and
eigenvalues of the Laplacian on an Einstein manifold.Comment: 28 pages, LaTe
On the supersymmetries of anti de Sitter vacua
We present details of a geometric method to associate a Lie superalgebra with
a large class of bosonic supergravity vacua of the type AdS x X, corresponding
to elementary branes in M-theory and type II string theory.Comment: 16 page
Deformations of conformal theories and non-toric quiver gauge theories
We discuss several examples of non-toric quiver gauge theories dual to
Sasaki-Einstein manifolds with U(1)^2 or U(1) isometry. We give a general
method for constructing non-toric examples by adding relevant deformations to
the toric case. For all examples, we are able to make a complete comparison
between the prediction for R-charges based on geometry and on quantum field
theory. We also give a general discussion of the spectrum of conformal
dimensions for mesonic and baryonic operators for a generic quiver theory; in
the toric case we make an explicit comparison between R-charges of mesons and
baryons.Comment: 51 pages, 12 figures; minor corrections in appendix B, published
versio
- …