gravity, supergravity

Formalism

• Poincaré Lie algebra

  • super Poincaré Lie algebra, supergravity Lie 3-algebra, supergravity Lie 6-algebra

• differential geometry

• (super-)Cartan geometry

  • pseudo-Riemannian manifold

  • spacetime

Definition

• Einstein-Hilbert action, Einstein's equations, general relativity

  • first-order formulation of gravity, D'Auria-Fre formulation of supergravity

  • gravity as a BF-theory, Plebanski formulation of gravity, teleparallel gravity

Spacetime configurations

• spacetime

• Minkowski spacetime

• black hole spacetime

  • Schwarzschild spacetime

  • Kerr spacetime

Properties

• Kaluza-Klein mechanism

• Bekenstein-Hawking entropy

• generalized second law of thermodynamics

• cosmic censorship hypothesis

• weak gravity conjecture

Spacetimes

• standard model of cosmology

• Minkowski spacetime

\linebreak

\linebreak

• asymptotically flat spacetime

• gravitational wave

• anti de Sitter spacetime

• FRW spacetime

• Taub-NUT spacetime

• Einstein manifold

• pp-wave spacetime

• KK-monopole

• Malament–Hogarth spacetime

• super spacetime

  • super Minkowski spacetime

• black brane

Quantum theory

• quantum gravity

  • graviton, gravitino

  • string theory

differential cohomology

Ingredients

• cohomology

• differential geometry

Connections on bundles

• connection on a bundle

  • parallel transport, holonomy

• curvature

  • curvature characteristic form, Chern character

• Chern-Weil theory

  • Chern-Weil homomorphism

  • secondary characteristic class

  • differential characteristic class

Higher abelian differential cohomology

• differential function complex

• differential orientation

• ordinary differential cohomology

  • differential Thom class

  • differential characters,

  • Deligne cohomology

  • circle n-bundle with connection,

  • bundle gerbe with connection

• differential K-theory

• differential elliptic cohomology

• differential cobordism cohomology

Higher nonabelian differential cohomology

• principal 2-bundle, principal ∞-bundle

• connection on a 2-bundle, connection on an ∞-bundle

• Chern-Weil theory in Smooth∞Grpd

  • ∞-Lie algebra cohomology

• ∞-Chern-Simons theory

Fiber integration

• higher holonomy

• fiber integration in differential cohomology

  • fiber integration in ordinary differential cohomology

  • fiber integration in differential K-theory

Application to gauge theory

• gauge theory

• gauge field

  • electromagnetic field

  • Yang-Mills field

  • Kalb-Ramond field/B-field

  • RR-field

  • supergravity C-field

  • supergravity

• quantum anomaly

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

• (higher) category theory and physics

• geometry of physics

• books and reviews, physics resources

theory (physics), model (physics)

experiment, measurement, computable physics

• mechanics

  • mass, charge, momentum, angular momentum, moment of inertia

  • dynamics on Lie groups

    • rigid body dynamics

• field (physics)

  • Lagrangian mechanics

    • configuration space, state

    • action functional, Lagrangian

    • covariant phase space, Euler-Lagrange equations

  • Hamiltonian mechanics

    • phase space

    • symplectic geometry

      • Poisson manifold

      • symplectic manifold

      • symplectic groupoid

    • multisymplectic geometry

      • n-symplectic manifold

  • spacetime

    • smooth Lorentzian manifold

    • special relativity

    • general relativity

    • gravity

      • supergravity, dilaton gravity

      • black hole

• Classical field theory

  • classical physics

    • classical mechanics
    • waves and optics
    • thermodynamics

• Quantum Mechanics

  • in terms of ∞-compact categories

  • quantum information

  • Hamiltonian operator

  • density matrix

  • Kochen-Specker theorem

  • Bell's theorem

  • Gleason's theorem

• Quantization

  • geometric quantization

  • deformation quantization

  • path integral quantization

  • semiclassical approximation

• Quantum Field Theory

  • Axiomatizations

    • algebraic QFT

      • Wightman axioms

      • Haag-Kastler axioms

        • operator algebra

        • local net

      • conformal net

      • Reeh-Schlieder theorem

      • Osterwalder-Schrader theorem

      • PCT theorem

      • Bisognano-Wichmann theorem

        • modular theory

      • spin-statistics theorem

        • boson, fermion

    • functorial QFT

      • cobordism

      • (∞,n)-category of cobordisms

      • cobordism hypothesis-theorem

      • extended topological quantum field theory

  • Tools

    • perturbative quantum field theory, vacuum

    • effective quantum field theory

    • renormalization

    • BV-BRST formalism

    • geometric ∞-function theory

  • particle physics

    • phenomenology

    • models

      • standard model of particle physics

      • fields and quanta

      • Grand Unified Theories, MSSM

    • scattering amplitude

      • on-shell recursion, KLT relations

  • Structural phenomena

    • universality class

    • quantum anomaly

      • Green-Schwarz mechanism

    • instanton

    • spontaneously broken symmetry

    • Kaluza-Klein mechanism

    • integrable systems

    • holonomic quantum fields

  • Types of quantum field thories

    • TQFT

      • 2d TQFT

      • Dijkgraaf-Witten theory

      • Chern-Simons theory

    • TCFT

      • A-model, B-model

      • homological mirror symmetry

    • QFT with defects

    • conformal field theory

    • (1,1)-dimensional Euclidean field theories and K-theory

    • (2,1)-dimensional Euclidean field theory and elliptic cohomology

    • CFT

      • WZW model

      • 6d (2,0)-supersymmetric QFT

    • gauge theory

      • field strength

      • gauge group, gauge transformation, gauge fixing

      • examples

        • electromagnetic field, QED

      • electric charge

      • magnetic charge

        • Yang-Mills field, QCD

      • Yang-Mills theory

      • spinors in Yang-Mills theory

      • topological Yang-Mills theory

        • Kalb-Ramond field
        • supergravity C-field
        • RR field
        • first-order formulation of gravity

      • general covariance

      • supergravity

      • D'Auria-Fre formulation of supergravity

      • gravity as a BF-theory

    • sigma-model

      • particle, relativistic particle, fundamental particle, spinning particle, superparticle

      • string, spinning string, superstring

      • membrane

      • AKSZ theory

• String Theory

  • string theory results applied elsewhere

• number theory and physics

  • Riemann hypothesis and physics