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59
Exact halfBPS type IIB interface solutions I: Local solution and supersymmetric Janus
, 2007
"... The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold AdS4 × S 2 × S 2 × Σ with SO(2,3) × SO(3) × SO(3) symmetry in terms of two holomorphic functions on a Riemann surface Σ, which generally has a boundary. This is achieved by reducing the BPS equations ..."
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Cited by 73 (14 self)
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The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold AdS4 × S 2 × S 2 × Σ with SO(2,3) × SO(3) × SO(3) symmetry in terms of two holomorphic functions on a Riemann surface Σ, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and SineGordon theories, and mapping this integrable system to a linear equation which can be solved exactly. Amongst the infinite class of solutions, a nonsingular Janus solution is identified which provides the AdS/CFT dual of the maximally supersymmetric YangMills interface theory discovered recently. The construction of general classes of globally nonsingular solutions, including fully backreacted AdS5 ×S 5 and supersymmetric Janus doped with D5 and/or NS5 branes,
The Killing superalgebra of tendimensional supergravity backgrounds
"... Abstract. We construct the Killing superalgebra of supersymmetric backgrounds of tendimensional heterotic and type II supergravities and prove that it is a Lie superalgebra. We also show that if the fraction of supersymmetry preserved by the background is greater than 1/2, in the heterotic case, or ..."
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Cited by 32 (3 self)
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Abstract. We construct the Killing superalgebra of supersymmetric backgrounds of tendimensional heterotic and type II supergravities and prove that it is a Lie superalgebra. We also show that if the fraction of supersymmetry preserved by the background is greater than 1/2, in the heterotic case, or greater than 3/4 in the type II case, then the background is locally homogeneous. Contents
Systematics of Mtheory spinorial geometry
, 2005
"... 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 s ..."
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Cited by 25 (11 self)
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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 of 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 elevendimensional supergravity can be found by solving a linear system. We The last ten years, the supersymmetric solutions of ten and eleven dimensional supergravities
The G2 spinorial geometry of supersymmetric IIB backgrounds
, 2005
"... We solve the Killing spinor equations of supersymmetric IIB backgrounds which admit one supersymmetry and the Killing spinor has stability subgroup G2 in Spin(9,1) × U(1). We find that such backgrounds admit a timelike Killing vector field and the geometric structure of the spacetime reduces from ..."
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Cited by 20 (11 self)
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We solve the Killing spinor equations of supersymmetric IIB backgrounds which admit one supersymmetry and the Killing spinor has stability subgroup G2 in Spin(9,1) × U(1). We find that such backgrounds admit a timelike Killing vector field and the geometric structure of the spacetime reduces from Spin(9,1) × U(1) to G2. We determine the type of G2 structure that the spacetime admits by computing the covariant derivatives of the spacetime forms associated with the Killing spinor bilinears. We also solve the Killing spinor equations of backgrounds with two supersymmetries and Spin(7) ⋉ R 8invariant spinors, and four supersymmetries with SU(4)⋉R 8 and with G2invariant spinors. We show that the Killing spinor equations factorize in two sets, one involving the geometry and the fiveform flux, and the other the threeform flux and the scalars. In the Spin(7)⋉R 8 and SU(4)⋉R 8 cases, the spacetime admits a parallel null vector field and so the spacetime metric can be locally described in terms of Penrose coordinates adapted to the associated
Systematics of IIB spinorial geometry
, 2005
"... We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hepth/0503046] to IIB supergravity. We give ..."
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Cited by 19 (8 self)
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We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hepth/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of the functions that determine the Killing spinors. This system can be solved to express the fluxes in terms of the geometry and determine the conditions on the geometry of any supersymmetric background. Similarly, the integrability conditions of the Killing spinor equations are turned into a linear system. This can be used to determine the field equations that are implied by the Killing spinor equations for any supersymmetric background. We show that these linear systems simplify for generic backgrounds with maximal and halfmaximal number of Hinvariant Killing spinors, H ⊂ Spin(9,1). In the maximal case, the
Geometry of fourdimensional Killing spinors
 JHEP 0707 (2007) 046 [arXiv:0704.0247 [hepth
"... Abstract: The supersymmetric solutions of N = 2, D = 4 minimal ungauged and gauged supergravity are classified according to the fraction of preserved supersymmetry using spinorial geometry techniques. Subject to a reasonable assumption in the 1/2supersymmetric timelike case of the gauged theory, w ..."
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Cited by 13 (5 self)
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Abstract: The supersymmetric solutions of N = 2, D = 4 minimal ungauged and gauged supergravity are classified according to the fraction of preserved supersymmetry using spinorial geometry techniques. Subject to a reasonable assumption in the 1/2supersymmetric timelike case of the gauged theory, we derive the complete form of all supersymmetric solutions. This includes a number of new 1/4 and 1/2supersymmetric possibilities, like gravitational waves on bubbles of nothing in AdS4.
GauduchonTod structures, Sim holonomy and De Sitter supergravity
, 2009
"... spinors are considered, using spinorial geometry techniques. It is shown that the “null ” solutions are defined in terms of a one parameter family of 3dimensional constrained EinsteinWeyl spaces called GauduchonTod structures. They admit a geodesic, expansionfree, twistfree and shearfree null ..."
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Cited by 6 (4 self)
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spinors are considered, using spinorial geometry techniques. It is shown that the “null ” solutions are defined in terms of a one parameter family of 3dimensional constrained EinsteinWeyl spaces called GauduchonTod structures. They admit a geodesic, expansionfree, twistfree and shearfree null vector field and therefore are a particular type of Kundt geometry. When the GauduchonTod structure reduces to the 3sphere, the null vector becomes recurrent, and therefore the holonomy is contained in Sim(3), the maximal proper subgroup of the Lorentz group SO(4, 1). For these geometries, all scalar invariants built from the curvature are constant.
KillingYano equations and Gstructures
, 712
"... We solve the KillingYano equation on manifolds with a Gstructure for G = SO(n),U(n),SU(n),Sp(n)·Sp(1),Sp(n),G2 and Spin(7). Solutions include nearlyKähler, weak holonomy G2, balanced SU(n) and holonomy G manifolds. As an application, we find that particle probes on AdS4 × X compactifications of t ..."
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Cited by 5 (1 self)
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We solve the KillingYano equation on manifolds with a Gstructure for G = SO(n),U(n),SU(n),Sp(n)·Sp(1),Sp(n),G2 and Spin(7). Solutions include nearlyKähler, weak holonomy G2, balanced SU(n) and holonomy G manifolds. As an application, we find that particle probes on AdS4 × X compactifications of type IIA and 11dimensional supergravity admit a Wtype of symmetry generated by the fundamental forms. We also explore the Wsymmetries of string and particle actions in heterotic and common sector supersymmetric backgrounds. In the heterotic case, the generators of the Wsymmetries completely characterize the solutions of the gravitino Killing spinor equation, and the structure constants of the Wsymmetry algebra depend on the solution of the dilatino Killing spinor equation. 1