Generating branes via sigma-models

Abstract

Starting with the D-dimensional Einstein-dilaton-antisymmetric form equations and assuming a block-diagonal form of a metric we derive a $(D-d)$-dimensional $\sigma$-model with the target space $SL(d,R)/SO(d)\times SL(2,R)/SO(2)\times R$ or its non-compact form. Various solution-generating techniques are developed and applied to construct some known and some new $p$-brane solutions. It is shown that the Harrison transformation belonging to the $SL(2,R)$ subgroup generates black $p$-branes from the seed Schwarzschild solution. A fluxbrane generalizing the Bonnor-Melvin-Gibbons-Maeda solution is constructed as well as a non-linear superposition of the fluxbrane and a spherical black hole. A new simple way to endow branes with additional internal structure such as plane waves is suggested. Applying the harmonic maps technique we generate new solutions with a non-trivial shell structure in the transverse space (`matrioshka' $p$-branes). It is shown that the $p$-brane intersection rules have a simple geometric interpretation as conditions ensuring the symmetric space property of the target space. Finally, a Bonnor-type symmetry is used to construct a new magnetic 6-brane with a dipole moment in the ten-dimensional IIA theory.

21 pages Latex

References in corpus (10)

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Cited by in corpus (63)

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• Special Geometry of Euclidean Supersymmetry I: Vector Multiplets
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• Exact solutions in multidimensional gravity with antisymmetric forms
• Special geometry of Euclidean supersymmetry II: hypermultiplets and the c-map
• Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes
• New nonuniform black string solutions
• Electrically charged dilatonic black rings
• Higher dimensional black holes in external magnetic fields
• Solutions with intersecting p-branes related to Toda chains
• Black holes in supergravity and integrability
• Non-extremal Black Holes, Harmonic Functions, and Attractor Equations
• Toda p-brane black holes and polynomials related to Lie algebras
• The full integration of black hole solutions to symmetric supergravity theories
• Magnetized black holes and black rings in the higher dimensional dilaton gravity
• Rotating non-asymptotically flat black rings in charged dilaton gravity
• Composite fluxbranes with general intersections
• Instantons, black holes and harmonic functions
• Supergravity Fluxbranes in Various Dimensions
• $d\ge 5$ static black holes with $S^2\times S^{d-4}$ event horizon topology
• Distorted Five-dimensional Electrically Charged Black Holes
• Black branes on the linear dilaton background
• Harrison transformation and charged black objects in Kaluza-Klein theory
• Static near-horizon geometries in five dimensions
• Black Holes, Moduli, and Long-Range Forces
• Charged Tachyons and Gauge Symmetry Breaking
• SL(4,R) generating symmetry in five-dimensional gravity coupled to dilaton and three-form
• On multidimensional analogs of Melvin's solution for classical series of Lie algebras
• Electric/magnetic universe with a cosmological constant
• More on general $p$-brane solutions
• Intersecting Non-extreme p-Branes and Linear Dilaton Background
• Black hole p-brane solutions for general intersection rules
• Static spacetimes haunted by a phantom scalar field II: dilatonic charged solutions
• Distorted stationary rotating black holes
• Special Geometry, Hessian Structures and Applications
• Supergravity p-branes revisited: extra parameters, uniqueness, and topological censorship
• Black holes as generalised Toda molecules
• Rotating dyonic dipole black rings: exact solutions and thermodynamics
• Inverse dualisation and non-local dualities between Einstein gravity and supergravities
• On calculation of fluxbrane polynomials corresponding to classical series of Lie algebras
• On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
• $d\ge 5$ magnetized static, balanced black holes with $S^2\times S^{d-4}$ event horizon topology
• On generalized Melvin solution for the Lie algebra $E_6$
• Static charged double-black rings in five dimensions
• On generalized Melvin solutions for Lie algebras of rank 3
• Higher-dimensional Buchdahl and Janis-Robinson-Winicour transformations in the Einstein-Maxwell system with a massless scalar field
• Supergravities on Branes
• Fluxbrane and S-brane solutions with polynomials related to rank-2 Lie algebras
• Cohomogeneity-1 solutions in Einstein-Maxwell-dilaton gravity
• On Brane Solutions Related to Non-Singular Kac-Moody Algebras
• The effective sigma-model of multidimensional gravity
• On Symmetries of Target Space for Sigma-model of p-brane Origin
• Brane solutions and integrability: a status report
• Exact solutions in gravity with a sigma model source
• Caged black hole with Maxwell charge
• Solenoid configurations and gravitational free energy of the AdS--Melvin spacetime
• On generalized Melvin solutions for Lie algebras of rank 4
• F0 fluxbranes, F-walls and new brane worlds
• Fluxbrane polynomials and Melvin-like solutions for simple Lie algebras
• On fluxbrane polynomials for generalized Melvin-like solutions associated with rank 5 Lie algebras
• Supergravity $p$-branes with scalar charge
• Weyl-type solutions with multipolar scalar fields