Gravity and Strings 1st edition by Tomás Ortín 0511189241 9780511189241

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ISBN 10 : 0511189241 

ISBN 13 : 9780511189241

Author:  Tomás Ortín 

One appealing feature of string theory is that it provides a theory of quantum gravity. Gravity and Strings is a self-contained, pedagogical exposition of this theory, its foundations and its basic results. In Part I, the foundations are traced back to the very early special-relativistic field theories of gravity, showing how such theories lead to general relativity. Gauge theories of gravity are then discussed and used to introduce supergravity theories. In Part II, some of the most interesting solutions of general relativity and its generalizations are studied. The final Part presents and studies string theory from the effective action point of view, using the results found earlier in the book as background. This 2004 book will be useful as a reference book for graduate students and researchers, as well as a complementary textbook for courses on gravity, supergravity and string theory.

Gravity and Strings 1st Table of contents:

Part I Introduction to gravity and supergravity
1 Differential geometry
1.1 World tensors
1.2 Affinely connected spacetimes
1.3 Metric spaces
1.3.1 Riemann–Cartan spacetime Ud
1.3.2 Riemann spacetime Vd
1.4 Tangent space
1.4.1 Weitzenböck spacetime Ad
1.5 Killing vectors
1.6 Duality operations
1.7 Differential forms and integration
1.8 Extrinsic geometry
2 Noether’s theorems
2.1 Equations of motion
2.2 Noether’s theorems
2.3 Conserved charges
2.4 The special-relativistic energy–momentum tensor
2.4.1 Conservation of angular momentum
2.4.2 Dilatations
2.4.3 Rosenfeld’s energy–momentum tensor
3 A perturbative introduction to general relativity
3.1 Scalar SRFTs of gravity
3.1.1 Scalar gravity coupled to matter
3.1.2 The action for a relativistic massive point-particle
3.1.3 The massive point-particle coupled to scalar gravity
3.1.4 The action for a massless point-particle
3.1.5 The massless point-particle coupled to scalar gravity
3.1.6 Self-coupled scalar gravity
3.1.7 The geometrical Einstein–Fokker theory
3.2 Gravity as a self-consistent massless spin-2 SRFT
3.2.1 Gauge invariance, gauge identities, and charge conservation in the SRFT of a spin-1 particle
3.2.2 Gauge invariance, gauge identities, and charge conservation in the SRFT of a spin-2 particle
3.2.3 Coupling to matter
3.2.4 The consistency problem
3.2.5 The Noether method for gravity
3.2.6 Properties of the gravitational energy–momentum tensor…
3.2.7 Deser’s argument
3.3 General relativity
3.4 The Fierz–Pauli theory in a curved background
3.4.1 Linearized gravity
3.4.2 Massless spin-2 particles in curved backgrounds
3.4.3 Self-consistency
3.5 Final Comments
4 Action principles for gravity
4.1 The Einstein–Hilbert action
4.1.1 Equations of motion
4.1.2 Gauge identity and Noether current
4.1.3 Coupling to matter
4.2 The Einstein–Hilbert action in different conformal frames
4.3 The first-order (Palatini) formalism
4.3.1 The purely affine theory
4.4 The Cartan–Sciama–Kibble theory
4.4.1 The coupling of gravity to fermions
4.4.2 The coupling to torsion: the CSK theory
4.4.3 Gauge identities and Noether currents
4.4.4 The first-order Vielbein formalism
4.5 Gravity as a gauge theory
4.6 Teleparallelism
4.6.1 The linearized limit
5 N = 1, 2, d = 4 supergravities
5.1 Gauging N = 1, d = 4 superalgebras
5.2 N = 1, d = 4 (Poincaré) supergravity
5.2.1 Local supersymmetry algebra
5.3 N = 1, d = 4 AdS supergravity
5.3.1 Local supersymmetry algebra
5.4 Extended supersymmetry algebras
5.4.1 Central extensions
5.5 N = 2, d = 4 (Poincaré) supergravity
5.6 N = 2, d = 4 “gauged” (AdS) supergravity
5.6.1 The local supersymmetry algebra
5.7 Proofs of some identities
6 Conserved charges in general relativity
6.1 The traditional approach
6.1.1 The Landau–Lifshitz pseudotensor
6.1.2 The Abbott–Deser approach
6.2 The Noether approach
6.3 The positive-energy theorem
Part II Gravitating point-particles
7 The Schwarzschild black hole
7.1 Schwarzschild’s solution
7.1.1 General properties
7.2 Sources for Schwarzschild’s solution
7.3 Thermodynamics
7.4 The Euclidean path-integral approach
7.4.1 The Euclidean Schwarzschild solution
7.4.2 The boundary terms
7.5 Higher-dimensional Schwarzschild metrics
7.5.1 Thermodynamics
8 The Reissner–Nordström black hole
8.1 Coupling a scalar field to gravity and no-hair theorems
8.2 The Einstein–Maxwell system
8.2.1 Electric charge
8.2.2 Massive electrodynamics
8.3 The electric Reissner–Nordström solution
8.4 The Sources of the electric RN black hole
8.5 Thermodynamics of RN black holes
8.6 The Euclidean electric RN solution and its action
8.7 Electric-magnetic duality
8.7.1 Poincar duality
8.7.2 Magnetic charge: the Dirac monopole and the Dirac quantization condition
8.7.3 The Wu–Yang monopole
8.7.4 Dyons and the DSZ charge-quantization condition
8.7.5 Duality in massive electrodynamics
8.8 Magnetic and dyonic RN black holes
8.9 Higher-dimensional RN solutions
9 The Taub–NUT solution
9.1 The Taub–NUT solution
9.2 The Euclidean Taub–NUT solution
9.2.1 Self-dual gravitational instantons
9.2.2 The BPST instanton
9.2.3 Instantons and monopoles
9.2.4 The BPST instanton and the KK monopole
9.2.5 Bianchi IX gravitational instantons
9.3 Charged Taub–NUT solutions and IWP solutions
10 Gravitational pp-waves
10.1 pp-Waves
10.1.1 Hpp-waves
10.2 Four-dimensional pp-wave solutions
10.2.1 Higher-dimensional pp-waves
10.3 Sources: the AS shock wave
11 The Kaluza–Klein black hole
11.1 Classical and quantum mechanics on…
11.2 KK dimensional reduction on a circle S
11.2.1 The Scherk–Schwarz formalism
11.2.2 Newton’s constant and masses
11.2.3 KK reduction of sources: the massless particle
11.2.4 Electric–magnetic duality and the KK action
11.2.5 Reduction of the Einstein–Maxwell action and N = 1, d = 5 SUGRA
11.3 KK reduction and oxidation of solutions
11.3.1 ERN black holes
11.3.2 Dimensional reduction of the AS shock wave: the extreme electric KK black hole
11.3.3 Non-extreme Schwarzschild and RN black holes
11.3.4 Simple KK solution-generating techniques
11.4 Toroidal (Abelian) dimensional reduction
11.4.1 The 2-torus and the modular group
11.4.2 Masses, charges and Newton’s constant
11.5 Generalized dimensional reduction
11.5.1 Example 1: a real scalar
11.5.2 Example 2: a complex scalar
11.5.3 Example 3: an SL(2,R)/SO(2) σ-model
11.5.4 Example 4: Wilson lines and GDR
11.6 Orbifold compactification
12 Dilaton and dilaton/axion black holes
12.1 Dilaton black holes: the a-model
12.1.1 The a-model solutions in four dimensions
12.2 Dilaton/axion black holes
12.2.1 The general SWIP solution
12.2.2 Supersymmetric SWIP solutions
12.2.3 Duality properties of the SWIP solutions
12.2.4 N = 2, d = 4 SUGRA solutions
13 Unbroken supersymmetry
13.1 Vacuum and residual symmetries
13.2 Supersymmetric vacua and residual (unbroken) supersymmetries
13.2.1 Covariant Lie derivatives
13.2.2 Calculation of supersymmetry algebras
13.3 N = 1, 2, d = 4 vacuum supersymmetry algebras
13.3.1 The Killing-spinor integrability condition
13.3.2 The vacua of N = 1, d = 4 Poincar supergravity
13.3.3 The vacua of N = 1, d = 4 AdS4 supergravity
13.3.4 The vacua of N = 2, d = 4 Poincar supergravity
13.3.5 The vacua of N = 2, d = 4 AdS supergravity
13.4 The vacua of d = 5, 6 supergravities with eight supercharges
13.4.1 N = (1,0), d 6 supergravity
13.4.2 N = 1, d = 5 supergravity
13.4.3 Relation to the N = 2, d = 4 vacua
13.5 Partially supersymmetric solutions
13.5.1 Partially unbroken supersymmetry, supersymmetry bounds, and the superalgebra
13.5.2 Examples
Part III Gravitating extended objects of string theory
14 String theory
14.1 Strings
14.1.1 Superstrings
14.1.2 Green–Schwarz Actions
14.2 Quantum theories of strings
14.2.1 Quantization of free-bosonic-string theories
14.2.2 Quantization of free-fermionic-string theories
14.2.3 D-Branes and O-planes in superstring theories
14.2.4 String interactions
14.3 Compactification on S1: T duality and D-branes
14.3.1 Closed bosonic strings on S1
14.3.2 Open bosonic strings on S1 and D-branes
14.3.3 Superstrings on S1
15 The string effective action and T duality
15.1 Effective actions and background fields
15.1.1 The D-brane effective action
15.2 T duality and background fields: Buscher’s rules
15.2.1 T duality in the bosonic-string effective action
15.2.2 T duality in the bosonic-string worldsheet action
15.2.3 T duality in the bosonic Dp-brane effective action
15.3 Example: the fundamental string (F1)
16 From eleven to four dimensions
16.1 Dimensional reduction from d = 11 to d = 10
16.1.1 11-dimensional supergravity
16.1.2 Reduction of the bosonic sector
16.1.3 Magnetic potentials
16.1.4 Reduction of fermions and the supersymmetry rules
16.2 Romans’ massive N = 2A, d = 10 supergravity
16.3 Further reduction of N = 2A, d = 10 SUEGRA to nine dimensions
16.3.1 Dimensional reduction of the bosonic RR sector
16.3.2 Dimensional reduction of fermions and supersymmetry rules
16.4 The effective-field theory of the heterotic string
16.5 Toroidal compactification of the heterotic string
16.5.1 Reduction of the action of pure N = 1, d = 10 supergravity
16.5.2 Reduction of the fermions and supersymmetry rules of N = 1, d = 10 SUGRA
16.5.3 The truncation to pure supergravity
16.5.4 Reduction with additional U(1) vector fields
16.5.5 Trading the KR 2-form for its dual
16.6 T duality, compactification, and supersymmetry
17 The type-IIB superstring and type-II T duality
17.1 N = 2B, d = 10 supergravity in the string frame
17.1.1 Magnetic potentials
17.1.2 The type-IIB supersymmetry rules
17.2 Type-IIB S duality
17.3 Dimensional reduction of N = 2B, d = 10 SUEGRA and type-II T duality
17.3.1 The type-II T-duality Buscher rules
17.4 Dimensional reduction of fermions and supersymmetry rules
17.5 Consistent truncations and heterotic/type-I duality
18 Extended objects
Introduction
18.1 Generalities
18.1.1 Worldvolume actions
18.1.2 Charged branes and Dirac charge quantization for extended objects
18.1.3 The coupling of p-branes to scalar fields
18.2 General p-brane solutions
18.2.1 Schwarzschild black p-branes
18.2.2 The p-brane a-model
18.2.3 Sources for solutions of the p-brane a-model
19 The extended objects of string theory
19.1 String-theory extended objects from duality
19.1.1 The masses of string- and M-theory extended objects from duality
19.2 String-theory extended objects from effective-theory solutions
19.2.1 Extreme p-brane solutions of string and M-theories and sources
19.2.2 The M2 solution
19.2.3 The M5 solution
19.2.4 The fundamental string F1
19.2.5 The S5 solution
19.2.6 The Dp-branes
19.2.7 The D-instanton
19.2.8 The D7-brane and holomorphic (d – 3)-branes
19.2.9 Some simple generalizations
19.3 The masses and charges of the p-brane solutions
19.3.1 Masses
19.3.2 Charges
19.4 Duality of string-theory solutions
19.4.1 N = 2A, d = 10 SUEGRA solutions from d = 11 SUGRA solutions
19.4.2 N 2A/B, d = 10 SUEGRA T-dual solutions
19.4.3 S duality of N = 2B, d = 10 SUEGRA solutions: pq-branes
19.5 String-theory extended objects from superalgebras
19.5.1 Unbroken supersymmetries of string-theory solutions
19.6 Intersections
19.6.1 Brane-charge conservation and brane surgery
19.6.2 Marginally bound supersymmetric states and intersections
19.6.3 Intersecting-brane solutions
19.6.4 The (a1–a2) model for p1- and p2-branes and black intersecting branes
20 String black holes in four and five dimensions
20.1 Composite dilaton black holes
20.2 Black holes from branes
20.2.1 Black holes from single wrapped branes
20.2.2 Black holes from wrapped intersecting branes
20.2.3 Duality and black-hole solutions
20.3 Entropy from microstate counting

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