Supersymmetric Solutions in Six Dimensions: A Linear Structure

Abstract

The equations underlying all supersymmetric solutions of six-dimensional minimal ungauged supergravity coupled to an anti-self-dual tensor multiplet have been known for quite a while, and their complicated non-linear form has hindered all attempts to systematically understand and construct BPS solutions. In this paper we show that, by suitably re-parameterizing these equations, one can find a structure that allows one to construct supersymmetric solutions by solving a sequence of linear equations. We then illustrate this method by constructing a new class of geometries describing several parallel spirals carrying D1, D5 and P charge and parameterized by four arbitrary functions of one variable. A similar linear structure is known to exist in five dimensions, where it underlies the black hole, black ring and corresponding microstate geometries. The unexpected generalization of this to six dimensions will have important applications to the construction of new, more general such geometries.

v2: Eqs. (2.1), (2.39) corrected, references added. v3: minor corrections

References in corpus (8)

• The fuzzball proposal for black holes
• Black Holes as Effective Geometries
• Mergers and Typical Black Hole Microstates
• Plumbing the Abyss: Black Ring Microstates
• Double, Double Supertube Bubble
• A class of BPS time-dependent 3-charge microstates from spectral flow
• Spinorial geometry and Killing spinor equations of 6-D supergravity
• 6D Dyonic String With Active Hyperscalars

Cited by in corpus (54)

• Habemus Superstratum! A constructive proof of the existence of superstrata
• Exotic Branes in String Theory
• Asymptotically-flat supergravity solutions deep inside the black-hole regime
• Momentum Fractionation on Superstrata
• 6D microstate geometries from 10D structures
• Superdescendants of the D1D5 CFT and their dual 3-charge geometries
• Superstratum Symbiosis
• Holomorphic Waves of Black Hole Microstructure
• M-theory Superstrata and the MSW String
• Integrability and Black-Hole Microstate Geometries
• Superstrata
• Effect of the twist operator in the D1D5 CFT
• Black-Hole Entropy from Supergravity Superstrata States
• AdS${}_3$ Holography at Dimension Two
• Bogoliubov coefficients for the twist operator in the D1D5 CFT
• Early Scrambling and Capped BTZ Geometries
• Oscillating supertubes and neutral rotating black hole microstates
• Supercharged AdS${}_3$ Holography
• Structure of Six-Dimensional Microstate Geometries
• Doubly-Fluctuating BPS Solutions in Six Dimensions
• Counting Superstrata
• Classification, geometry and applications of supersymmetric backgrounds
• Microstate Geometries from Gauged Supergravity in Three Dimensions
• Hair-brane Ideas on the Horizon
• Perturbative 3-charge microstate geometries in six dimensions
• Perturbative superstrata
• New Superstrata from Three-Dimensional Supergravity
• Three-charge superstrata with internal excitations
• Multi-Superthreads and Supersheets
• BPS Solutions of Six-Dimensional (1,0) Supergravity Coupled to Tensor Multiplets
• New Supersymmetric Bubbles on AdS_3xS^3
• Resolving Black-Hole Microstructure with New Momentum Carriers
• Supersymmetric Dyonic Strings in 6-Dimensions from 3-Dimensions
• The (amazing) Super-Maze
• Shockwaves in black hole microstate geometries
• The Structure of BPS Equations for Ambi-polar Microstate Geometries
• The structure of all the supersymmetric solutions of ungauged N = (1,0),d=6 supergravity
• Cool horizons lead to information loss
• Contact metric three manifolds and Lorentzian geometry with torsion in six-dimensional supergravity
• Non-extremal superdescendants of the D1D5 CFT
• Microstate geometries at a generic point in moduli space
• Bound states of spinning black holes in five dimensions
• Non-Supersymmetric, Multi-Center Solutions with Topological Flux
• Corrugated Multi-Supersheets
• Codimension-2 Solutions in Five-Dimensional Supergravity
• Linearizing the BPS Equations with Vector and Tensor Multiplets
• Non-Abelian Supertubes
• Multi-center Superstrata
• From Static to Cosmological Solutions of N=2 Supergravity
• Solvable time-like cosets and holography beyond $AdS$
• Holographic entanglement entropy and complexity of microstate geometries
• Killing Spinors and Related Symmetries in Six Dimensions
• BPS equations and Non-trivial Compactifications
• Elliptical and Purely NS Superstrata