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Quantum Gravity
Quantum Gravity
Table of Contents
1 Introduction
1.1 Problems
1.2 Expected properties
1.2.1 No local observables
1.3 QFT in curved spacetime
1.3.1 Unruh radiation in flat space
1.3.2 Hawking radiation
1.3.3 The information paradox
1.3.3.1 The small corrections theorem
1.3.3.2 AMPS firewall
1.4 GR as a QFT
1.4.1 Perturbative
1.4.2 Euclidean gravitational path integral
1.4.3 Gravitational instantons
1.5 GR as an EFT
1.5.1 Universal quantum non-relativistic correction
1.5.2 Uncertainty in the causal structure light cones
I String theory
6.1 Classical
10.10.1 Noncommutative algebraic geometry
2.1 $D>2$
3.1 Classical quantum mechanics
9.2.1 Holographic entanglement entropy
13.1 Black holes
10.1 Mirror symmetry
9.1 AdS/CFT
11.1 Membrane theory
6.8.1 T-duality
7.1 String compactifications
11.2.1 BFSS matrix model
6.2 Quantize
4.2 Quantize
11.2 Matrix theory
9.2 It from Qubit AdS/CFT
13.1.2 Wormholes
12.2 Bosonic string field theory
2.2 $D=2$
13.2 Chern-Simons theories
5.2 SUSY QFT
6.3 Type II string theories
4.3 Scattering amplitudes
5.3 SUGRA
9.3 Flat space holography bottom-up approaches
13.3 Topological string theory
5.2.3 Supersymmetric localization
11.3 AdS/CFT approach
7.3 String cosmology
6.4 Type I string theory
13.4 More on scattering amplitudes
2.4 Renormalization group flow
7.4 Particle phenomenology
9.4 de Sitter holography approaches
6.5 Heterotic string theories
6.5.1 $SO(32)$ and $E_8 E_8$
6.5.2 Toroidal compactifications
6.5.3 $N=2$
7.5 Swampland
6.6 Vertex operators
9.1.6 Different dimensions
2.6 $4D$ superconformal field theories
8.7 Stringy AdS/CFT from $D$-branes
9.2.7 SYK
6.7 Scattering amplitudes
6.7.1 Tree-level amplitudes
6.7.2 One-loop amplitudes
6.7.3 UV finiteness
6.7.4 $l_s0$ $l_s$ $g_s 0$ limits
6.8 String dualities
6.8.2 S-duality
6.8.3 U-duality
6.8.4 F-theory
13.8 $2D$ theories
10.9 Higher structures
2.9 Bootstrap in $D 3$
10.10 Noncommutative geometry
2.2.10 CFT on the Torus
10.11 Quantum groups
2.2.11 Boudary CFT
13.12 Other proposals for quantum spacetime
9.1.13 Holographic QCD
2 Conformal field theory
2.3 Conformal quantum mechanics
2.5 $3D$ superconformal Chern-Simons matter theories
2.7 $6D$ superconformal field theories
2.8 AGT correspondence
2.10 Nonrelativistic Schrödinger CFTs
2.11 Axiomatic CFT
2.12 Conformal geometry
3 Worldline formalism ($$ tension limit)
3.2 Perturbative QFT (sum over worldlines)
3.3 Worldline nonperturbative QFT
3.4 Gravity
3.5 Non-geometric target space
4 Bosonic string theory
4.1 Classical bosonic string
5 Supersymmetry
5.1 SUSY QM
6 Superstring theory
7 String landscape
7.2 Nongeometric compactifications
8 $D$-branes
8.1 Effective actions
8.2 As BPS SUGRA solitons
8.3 D-branes moving and merging
8.4 Creation/Annihilation of D-branes
8.5 Multiple coincident D-branes
8.6 D-brane geometry
9 Holography
10 Stringy maths
10.2 Vertex Operator Algebras
10.3 Modular forms
10.4 Monstrous moonshine
10.5 Knot theory
10.6 Geometric Langlands correspondence
10.7 K-theory
10.8 p-adic strings
11 M-theory
11.4 Heterotic M-theory
11.5 Miscellaneous
12 String field theory
12.1 Off-shell string theory
12.3 Superstring field theory
12.4 Tachyon condensation
13 Miscellaneous
II Other approaches
13.5 Generalized symmetries
13.6 Pure spinor formalism
13.7 Nonrelativistic string theory
13.9 QCD Strings and Effective String Theories
13.10 Little string theory
13.11 Higher spin theory (tensionless limit)
13.13 Open problems in string theory
14 Twistor theory
14.1 Real slices and reality structures
14.2 $M_C$'s conformal structure $=PT$'s complex structure
14.3 Penrose transform
14.4 Gauge theory
14.5 Ambitwistors and $d>4$
14.6 Mini-Twistor theory
14.7 Miscellaneous
15 Canonical quantum gravity
15.1 ADM formalism
15.2 Wheeler–DeWitt equation
16 Loop quantum gravity
16.1 Ashtekar variables
16.2 Quantum Riemannian geometry
16.3 Spin foams
16.4 Black hole entropy
16.5 Loop quantum cosmology
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7.5.6 Finiteness and string lamppost
7.5.6 Finiteness and string lamppost
\subsubsection{The decoupling limit}
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