24 research outputs found
The geometry of extended null supersymmetry in M-theory
For supersymmetric spacetimes in eleven dimensions admitting a null Killing
spinor, a set of explicit necessary and sufficient conditions for the existence
of any number of arbitrary additional Killing spinors is derived. The necessary
and sufficient conditions are comprised of algebraic relationships, linear in
the spinorial components, between the spinorial components and their first
derivatives, and the components of the spin connection and four-form. The
integrability conditions for the Killing spinor equation are also analysed in
detail, to determine which components of the field equations are implied by
arbitrary additional supersymmetries and the four-form Bianchi identity. This
provides a complete formalism for the systematic and exhaustive investigation
of all spacetimes with extended null supersymmetry in eleven dimensions. The
formalism is employed to show that the general bosonic solution of eleven
dimensional supergravity admitting a structure defined by four Killing
spinors is either locally the direct product of with a
seven-manifold of holonomy, or locally the Freund-Rubin direct product of
with a seven-manifold of weak holonomy. In addition, all
supersymmetric spacetimes admitting a
structure are classified.Comment: 36 pages, latex; v2, section classifying all spacetimes admitting a
structure included; v3, typos
corrected. Final version to appear in Phys.Rev.
Nearing Extremal Intersecting Giants and New Decoupled Sectors in N = 4 SYM
We study near-horizon limits of near-extremal charged black hole solutions to
five-dimensional gauged supergravity carrying two charges, extending
the recent work of Balasubramanian et.al. We show that there are two
near-horizon decoupling limits for the near-extremal black holes, one
corresponding to the near-BPS case and the other for the far from BPS case.
Both of these limits are only defined on the 10d IIB uplift of the 5d black
holes, resulting in a decoupled geometry with a six-dimensional part (conformal
to) a rotating BTZ X . We study various aspects of these decoupling limits
both from the gravity side and the dual field theory side. For the latter we
argue that there should be two different, but equivalent, dual gauge theory
descriptions, one in terms of the 2d CFT's dual to the rotating BTZ and the
other as certain large R-charge sectors of d=4,N =4 U(N) SYM theory. We discuss
new BMN-type sectors of the N=4 SYM in the limit in which the
engineering dimensions scale as (for the near-BPS case) and as
(for the far from BPS case).Comment: 44 pages, references added, minor change
On the smoothness of multi-M2 brane horizons
We calculate the degree of horizon smoothness of multi- -brane solution
with branes along a common axis. We find that the metric is generically only
thrice continuously differentiable at any of the horizons. The four-form field
strength is found to be only twice continuously differentiable. We work with
Gaussian null-like co-ordinates which are obtained by solving geodesic
equations for multi- brane geometry. We also find different, exact
co-ordinate transformations which take the metric from isotropic co-ordinates
to co-ordinates in which metric is thrice differentiable at the horizon. Both
methods give the same result that the multi- brane metric is only thrice
continuously differentiable at the horizon.Comment: 24 pages, reference added, modified equation for non-singularity of
metri
The complex geometry of holographic flows of quiver gauge theories
We argue that the complete Klebanov-Witten flow solution must be described by
a Calabi-Yau metric on the conifold, interpolating between the orbifold at
infinity and the cone over T^(1,1) in the interior. We show that the complete
flow solution is characterized completely by a single, simple, quasi-linear,
second order PDE, or "master equation," in two variables. We show that the
Pilch-Warner flow solution is almost Calabi-Yau: It has a complex structure, a
hermitian metric, and a holomorphic (3,0)-form that is a square root of the
volume form. It is, however, not Kahler. We discuss the relationship between
the master equation derived here for Calabi-Yau geometries and such equations
encountered elsewhere and that govern supersymmetric backgrounds with multiple,
independent fluxes.Comment: 26 pages, harvmac + amssy
Splitting hairs of the three charge black hole
We construct the large radius limit of the metric of three charge supertubes
and three charge BPS black rings by using the fact that supertubes preserve the
same supersymmetries as their component branes. Our solutions reproduce a few
of the properties of three charge supertubes found recently using the Born
Infeld description. Moreover, we find that these solutions pass a number of
rather nontrivial tests which they should pass if they are to describe some of
the hair of three charge black holes and three charge black rings.Comment: 15 pages, LaTeX, v2 minor correction
Are There Any New Vacua of Gauged N=8 Supergravity in Four Dimensions?
We consider the most general SU(3) singlet space of gauged N=8 supergravity
in four-dimensions. The SU(3)-invariant six scalar fields in the theory can be
viewed in terms of six real four-forms. By exponentiating these four-forms, we
eventually obtain the new scalar potential. For the two extreme limits, we
reproduce the previous results found by Warner in 1983. In particular, for the
N=1 G_2 critical point, we find the constraint surface parametrized by three
scalar fields on which the cosmological constant has the same value. We obtain
the BPS domain-wall solutions for restricted scalar submanifold. We also
describe the three-dimensional mass-deformed superconformal Chern-Simons matter
theory dual to the above supersymmetric flows in four-dimensions.Comment: 44p; the main text and appendices improved for compact
presentation;the acknowledgments added and to appear in IJMP
Symplectic potentials and resolved Ricci-flat ACG metrics
We pursue the symplectic description of toric Kahler manifolds. There exists
a general local classification of metrics on toric Kahler manifolds equipped
with Hamiltonian two-forms due to Apostolov, Calderbank and Gauduchon(ACG). We
derive the symplectic potential for these metrics. Using a method due to Abreu,
we relate the symplectic potential to the canonical potential written by
Guillemin. This enables us to recover the moment polytope associated with
metrics and we thus obtain global information about the metric. We illustrate
these general considerations by focusing on six-dimensional Ricci flat metrics
and obtain Ricci flat metrics associated with real cones over L^{pqr} and
Y^{pq} manifolds. The metrics associated with cones over Y^{pq} manifolds turn
out to be partially resolved with two blowup parameters taking special
(non-zero)values. For a fixed Y^{pq} manifold, we find explicit metrics for
several inequivalent blow-ups parametrised by a natural number k in the range
0<k<p. We also show that all known examples of resolved metrics such as the
resolved conifold and the resolution of C^3/Z_3 also fit the ACG
classification.Comment: LaTeX, 34 pages, 4 figures (v2)presentation improved, typos corrected
and references added (v3)matches published versio
N=8 Gauged Supergravity Theory and N=6 Superconformal Chern-Simons Matter Theory
By studying the previously known holographic N=4 supersymmetric
renormalization group flow(Gowdigere-Warner) in four dimensions, we find the
mass deformed Chern-Simons matter theory which has N=4 supersymmetry by adding
the four mass terms among eight adjoint fields. The geometric superpotential
from the eleven dimensions is found and provides the M2-brane probe analysis.
As second example, we consider known holographic N=8 supersymmetric
renormalization group flow(Pope-Warner) in four dimensions. The eight mass
terms are added and similar geometric superpotential is obtained.Comment: 39 pp; The footnotes 3 and 4 and the ref. added; improved the page 2
and to appear in IJMP
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
Deformations of flows from type IIB supergravity
We consider supersymmetric SL(3,R) deformations of various type IIB
supergravity backgrounds which exhibit flows away from an asymptotically
locally AdS_5 x S^5 fixed point. This includes the gravity dual of the Coulomb
branch of N=1 super Yang Mills theory, for which the deformed superpotential is
known. We also consider the gravity duals of field theories which live on
various curved backgrounds, such as Minkowski_2 x H^2, AdS_3 x S^1 and R x S^3.
Some of the deformed theories flow from a four-dimensional N=1 superconformal
UV fixed point to a two-dimensional (2,2) superconformal IR fixed point. We
study nonsupersymmetric generalizations of the deformations of the above
Coulomb branch flows.Comment: 29 pages, additional references and comment