19 research outputs found
A Note on Einstein Sasaki Metrics in D \ge 7
In this paper, we obtain new non-singular Einstein-Sasaki spaces in
dimensions D\ge 7. The local construction involves taking a circle bundle over
a (D-1)-dimensional Einstein-Kahler metric that is itself constructed as a
complex line bundle over a product of Einstein-Kahler spaces. In general the
resulting Einstein-Sasaki spaces are singular, but if parameters in the local
solutions satisfy appropriate rationality conditions, the metrics extend
smoothly onto complete and non-singular compact manifolds.Comment: Latex, 13 page
Beta, Dipole and Noncommutative Deformations of M-theory Backgrounds with One or More Parameters
We construct new M-theory solutions starting from those that contain 5 U(1)
isometries. We do this by reducing along one of the 5-torus directions, then
T-dualizing via the action of an O(4,4) matrix and lifting back to
11-dimensions. The particular T-duality transformation is a sequence of O(2,2)
transformations embedded in O(4,4), where the action of each O(2,2) gives a
Lunin-Maldacena deformation in 10-dimensions. We find general formulas for the
metric and 4-form field of single and multiparameter deformed solutions, when
the 4-form of the initial 11-dimensional background has at most one leg along
the 5-torus. All the deformation terms in the new solutions are given in terms
of subdeterminants of a 5x5 matrix, which represents the metric on the 5-torus.
We apply these results to several M-theory backgrounds of the type AdS_r x
X^{11-r}. By appropriate choices of the T-duality and reduction directions we
obtain analogues of beta, dipole and noncommutative deformations. We also
provide formulas for backgrounds with only 3 or 4 U(1) isometries and study a
case, for which our assumption for the 4-form field is violated.Comment: v2:minor corrections, v3:small improvements, v4:conclusions expanded,
to appear in Class. Quant. Gra
Supersymmetric AdS_5 solutions of M-theory
We analyse the most general supersymmetric solutions of D=11 supergravity
consisting of a warped product of five-dimensional anti-de-Sitter space with a
six-dimensional Riemannian space M_6, with four-form flux on M_6. We show that
M_6 is partly specified by a one-parameter family of four-dimensional Kahler
metrics. We find a large family of new explicit regular solutions where M_6 is
a compact, complex manifold which is topologically a two-sphere bundle over a
four-dimensional base, where the latter is either (i) Kahler-Einstein with
positive curvature, or (ii) a product of two constant-curvature Riemann
surfaces. After dimensional reduction and T-duality, some solutions in the
second class are related to a new family of Sasaki-Einstein spaces which
includes T^{1,1}/Z_2. Our general analysis also covers warped products of
five-dimensional Minkowski space with a six-dimensional Riemannian space.Comment: 40 pages. v2: minor changes, eqs. (2.22) and (D.12) correcte
Supersymmetric AdS_5 Solutions of Type IIB Supergravity
We analyse the most general bosonic supersymmetric solutions of type IIB
supergravity whose metrics are warped products of five-dimensional anti-de
Sitter space AdS_5 with a five-dimensional Riemannian manifold M_5. All fluxes
are allowed to be non-vanishing consistent with SO(4,2) symmetry. We show that
the necessary and sufficient conditions can be phrased in terms of a local
identity structure on M_5. For a special class, with constant dilaton and
vanishing axion, we reduce the problem to solving a second order non-linear
ODE. We find an exact solution of the ODE which reproduces a solution first
found by Pilch and Warner. A numerical analysis of the ODE reveals an
additional class of local solutions.Comment: 33 page
On the Ricci tensor in type II B string theory
Let be a metric connection with totally skew-symmetric torsion \T
on a Riemannian manifold. Given a spinor field and a dilaton function
, the basic equations in type II B string theory are \bdm \nabla \Psi =
0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi
= b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations
between the length ||\T||^2 of the torsion form, the scalar curvature of
, the dilaton function and the parameters . The main
results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the
connection. In particular, if the supersymmetry is non-trivial and if
the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d
\T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is
divergence-free. We show that the latter condition is satisfied in many
examples constructed out of special geometries. A special case is . Then
the divergence of the energy-momentum tensor vanishes if and only if one
condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T =
0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq
0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2
All supersymmetric solutions of minimal supergravity in six dimensions
A general form for all supersymmetric solutions of minimal supergravity in
six dimensions is obtained. Examples of new supersymmetric solutions are
presented. It is proven that the only maximally supersymmetric solutions are
flat space, AdS_3 x S^3 and a plane wave. As an application of the general
solution, it is shown that any supersymmetric solution with a compact horizon
must have near-horizon geometry R^{1,1} x T^4, R^{1,1} x K3 or identified AdS_3
x S^3.Comment: 40 pages. v2: two references adde
The general form of supersymmetric solutions of N=(1,0) U(1) and SU(2) gauged supergravities in six dimensions
We obtain necessary and sufficient conditions for a supersymmetric field
configuration in the N=(1,0) U(1) or SU(2) gauged supergravities in six
dimensions, and impose the field equations on this general ansatz. It is found
that any supersymmetric solution is associated to an structure. The structure is characterized by a null Killing
vector which induces a natural 2+4 split of the six dimensional spacetime. A
suitable combination of the field equations implies that the scalar curvature
of the four dimensional Riemannian part, referred to as the base, obeys a
second order differential equation. Bosonic fluxes introduce torsion terms that
deform the structure away from a covariantly
constant one. The most general structure can be classified in terms of its
intrinsic torsion. For a large class of solutions the gauge field strengths
admit a simple geometrical interpretation: in the U(1) theory the base is
K\"{a}hler, and the gauge field strength is the Ricci form; in the SU(2)
theory, the gauge field strengths are identified with the curvatures of the
left hand spin bundle of the base. We employ our general ansatz to construct
new supersymmetric solutions; we show that the U(1) theory admits a symmetric
Cahen-Wallach solution together with a compactifying pp-wave. The
SU(2) theory admits a black string, whose near horizon limit is . We also obtain the Yang-Mills analogue of the Salam-Sezgin solution of
the U(1) theory, namely , where the is supported by a
sphaleron. Finally we obtain the additional constraints implied by enhanced
supersymmetry, and discuss Penrose limits in the theories.Comment: 1+29 pages, late
Eguchi-Hanson Solitons in Odd Dimensions
We present a new class of solutions in odd dimensions to Einstein's equations
containing either a positive or negative cosmological constant. These solutions
resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added
feature of having Lorentzian signatures. They are asymptotic to
(A)dS. In the AdS case their energy is negative relative to that of
pure AdS. We present perturbative evidence in 5 dimensions that such metrics
are the states of lowest energy in their asymptotic class, and present a
conjecture that this is generally true for all such metrics. In the dS case
these solutions have a cosmological horizon. We show that their mass at future
infinity is less than that of pure dS.Comment: 26 pages, Late
Mesonic Chiral Rings in Calabi-Yau Cones from Field Theory
We study the half-BPS mesonic chiral ring of the N=1 superconformal quiver
theories arising from N D3-branes stacked at Y^pq and L^abc Calabi-Yau conical
singularities. We map each gauge invariant operator represented on the quiver
as an irreducible loop adjoint at some node, to an invariant monomial, modulo
relations, in the gauged linear sigma model describing the corresponding bulk
geometry. This map enables us to write a partition function at finite N over
mesonic half-BPS states. It agrees with the bulk gravity interpretation of
chiral ring states as cohomologically trivial giant gravitons. The quiver
theories for L^aba, which have singular base geometries, contain extra
operators not counted by the naive bulk partition function. These extra
operators have a natural interpretation in terms of twisted states localized at
the orbifold-like singularities in the bulk.Comment: Latex, 25pgs, 12 figs, v2: minor clarification