Black Holes and Higher Composition Laws

Abstract

We describe various relations between Bhargava's higher composition laws, which generalise Gauss's original composition law on integral binary quadratic forms, and extremal black hole solutions appearing in string/M-theory and related models. The cornerstone of these correspondences is the identification of the charge cube of the STU black hole with Bhargava's cube of integers, which underpins the related higher composition laws.

25 pages. References and further note added. Minor typos corrected

References in corpus (41)

• Dualisation of Dualities, I
• Four Dimensional String/String/String Triality
• Orbits of Exceptional Groups, Duality and BPS States in String Theory
• Arithmetic and Attractors
• STU Black Holes and String Triality
• Broken sigma-model isometries in very special geometry
• Four-qubit entanglement from string theory
• String triality, black hole entropy and Cayley's hyperdeterminant
• Universal BPS structure of stationary supergravity solutions
• Generating Geodesic Flows and Supergravity Solutions
• Higher-dimensional Origin of D=3 Coset Symmetries
• BPS black holes, quantum attractor flows and automorphic forms
• Black holes admitting a Freudenthal dual
• The black-hole/qubit correspondence: an up-to-date review
• Orbits and Attractors for N=2 Maxwell-Einstein Supergravity Theories in Five Dimensions
• stu Black Holes Unveiled
• Generalized Conformal and Superconformal Group Actions and Jordan Algebras
• A magic pyramid of supergravities
• Quantum Attractor Flows
• Small representations, string instantons, and Fourier modes of Eisenstein series (with an appendix by D. Ciubotaru and P. Trapa)
• N=8 non-BPS Attractors, Fixed Scalars and Magic Supergravities
• Complete construction of magical, symmetric and homogeneous N=2 supergravities as double copies of gauge theories
• Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups
• Freudenthal triple classification of three-qubit entanglement
• A magic square from Yang-Mills squared
• On the Black-Hole/Qubit Correspondence
• Wrapped branes as qubits
• Duality, Entropy and ADM Mass in Supergravity
• Degeneration of Groups of Type E7 and Minimal Coupling in Supergravity
• Freudenthal Duality and Generalized Special Geometry
• Unitary Realizations of U-duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories
• Gravitational multi-NUT solitons, Komar masses and charges
• Jordan algebras, exceptional groups, and higher composition laws
• Two-Center Black Holes Duality-Invariants for stu Model and its lower-rank Descendants
• Charge Orbits of Extremal Black Holes in Five Dimensional Supergravity
• Hidden symmetries of the Nambu-Goto action
• Freudenthal Dual Lagrangians
• Orbits in Non-Supersymmetric Magic Theories
• Green-Schwarz, Nambu-Goto Actions, and Cayley's Hyperdeterminant
• Freudenthal duality and conformal isometries of extremal black holes
• Freudenthal Duality in Gravity: from Groups of Type E7 to Pre-Homogeneous Spaces

Cited by in corpus (5)

• Arithmetic of decay walls through continued fractions: a new exact dyon counting solution in $\mathcal{N}=4$ CHL models
• M-theory, Black Holes and Cosmology
• BPS Black Hole Entropy and Attractors in Very Special Geometry. Cubic Forms, Gradient Maps and their Inversion
• Perturbative and non-pertrubative trace anomalies
• Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday