9 research outputs found
AdS spacetimes from wrapped D3-branes
We derive a geometrical characterisation of a large class of AdS_3 and AdS_2
supersymmetric spacetimes in IIB supergravity with non-vanishing five-form flux
using G-structures. These are obtained as special cases of a class of
supersymmetric spacetimes with an or (time)
factor that are associated with D3-branes wrapping calibrated 2- or 3- cycles,
respectively, in manifolds with SU(2), SU(3), SU(4) and G_2 holonomy. We show
how two explicit AdS solutions, previously constructed in gauged supergravity,
satisfy our more general G-structure conditions. For each explicit solution we
also derive a special holonomy metric which, although singular, has an
appropriate calibrated cycle. After analytic continuation, some of the classes
of AdS spacetimes give rise to known classes of BPS bubble solutions with
, , and
symmetry. These have 1/2, 1/4 and 1/8 supersymmetry,
respectively. We present a new class of 1/8 BPS geometries with
symmetry, obtained by analytic continuation of the
class of AdS spacetimes associated with D3-branes wrapped on associative
three-cycles.Comment: 1+30 pages; v2, references added; v3, typos corrected, reference
adde
Systematics of M-theory spinorial geometry
We reduce the classification of all supersymmetric backgrounds in eleven
dimensions to the evaluation of the supercovariant derivative and of an
integrability condition, which contains the field equations, on six types of
spinors. We determine the expression of the supercovariant derivative on all
six types of spinors and give in each case the field equations that do not
arise as the integrability conditions of Killing spinor equations. The Killing
spinor equations of a background become a linear system for the fluxes,
geometry and spacetime derivatives of the functions that determine the spinors.
The solution of the linear system expresses the fluxes in terms of the geometry
and specifies the restrictions on the geometry of spacetime for all
supersymmetric backgrounds. We also show that the minimum number of field
equations that is needed for a supersymmetric configuration to be a solution of
eleven-dimensional supergravity can be found by solving a linear system. The
linear systems of the Killing spinor equations and their integrability
conditions are given in both a timelike and a null spinor basis. We illustrate
the construction with examples.Comment: 46 pages. v2: systematics of a null spinor basis is included in
section
Beyond LLM in M-theory
The Lin, Lunin, Maldacena (LLM) ansatz in D = 11 supports two independent
Killing directions when a general Killing spinor ansatz is considered. Here we
show that these directions always commute, identify when the Killing spinors
are charged, and show that both their inner product and resulting geometry are
governed by two fundamental constants. In particular, setting one constant to
zero leads to AdS7 x S4, setting the other to zero gives AdS4 x S7, while flat
spacetime is recovered when both these constants are zero. Furthermore, when
the constants are equal, the spacetime is either LLM, or it corresponds to the
Kowalski-Glikman solution where the constants are simply the mass parameter.Comment: 1+30 pages, footnote adde
The spinorial geometry of supersymmetric backgrounds
We propose a new method to solve the Killing spinor equations of
eleven-dimensional supergravity based on a description of spinors in terms of
forms and on the Spin(1,10) gauge symmetry of the supercovariant derivative. We
give the canonical form of Killing spinors for N=2 backgrounds provided that
one of the spinors represents the orbit of Spin(1,10) with stability subgroup
SU(5). We directly solve the Killing spinor equations of N=1 and some N=2, N=3
and N=4 backgrounds. In the N=2 case, we investigate backgrounds with SU(5) and
SU(4) invariant Killing spinors and compute the associated spacetime forms. We
find that N=2 backgrounds with SU(5) invariant Killing spinors admit a timelike
Killing vector and that the space transverse to the orbits of this vector field
is a Hermitian manifold with an SU(5)-structure. Furthermore, N=2 backgrounds
with SU(4) invariant Killing spinors admit two Killing vectors, one timelike
and one spacelike. The space transverse to the orbits of the former is an
almost Hermitian manifold with an SU(4)-structure and the latter leaves the
almost complex structure invariant. We explore the canonical form of Killing
spinors for backgrounds with extended, N>2, supersymmetry. We investigate a
class of N=3 and N=4 backgrounds with SU(4) invariant spinors. We find that in
both cases the space transverse to a timelike vector field is a Hermitian
manifold equipped with an SU(4)-structure and admits two holomorphic Killing
vector fields. We also present an application to M-theory Calabi-Yau
compactifications with fluxes to one-dimension.Comment: Latex, 54 pages, v2: clarifications made and references added. v3:
minor changes. v4: minor change
1/2-BPS states in M theory and defects in the dual CFTs
We study supersymmetric branes in AdS_7 x S^4 and AdS_4 x S^7. We show that
in the former case the membranes should be viewed as M5 branes with fluxes and
we identify two types of such fivebranes (they are analogous to giant gravitons
and to dual giants). In AdS_4 x S^7 we find both M5 branes with fluxes and
freestanding stacks of membranes. We also go beyond probe approximation and
construct regular supergravity solutions describing geometries produced by the
branes. The metrics are completely specified by one function which satisfies
either Laplace or Toda equation and we give a complete classification of
boundary conditions leading to smooth geometries. The brane configurations
discussed in this paper are dual to various defects in three- and
six-dimensional conformal field theories.Comment: 82 pages, 12 figures, added ref