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Some theoretical physicists have what they see as an exciting new "theory of everything," string theory, that they feel will unify two seemingly diametrically opposed theories, quantum mechanics and general relativity. The theory of everything must unify nature's fundamental forces (gravitational, electromagnetic, and nuclear). Stephen Hawking is very interested in string theory. Gianguido Dall'Agata will be discussing the discovery of the SO(8) gauged theories of supergravity at King's College this month. This discussion has yet to take place and therefore is not a factor in this introductory book on strings and branes.
West in his discussion of string interactions, ultimately concludes that "One of the unusual aspects of string theory is that the theory used to calculate string scattering is often more complicated than the result itself, namely the the string scattering amplitudes." Throughout the book mathematical models are used to illustrate physics equations and formulae. Supersymmetric theories not discussed in the book can be found in West's complimentary book, Introduction to Supersymmetry and Supergravity. Additionally, topics not discussed in this book are Calabi-Yau Compactification (differential geometry required here), string-based black hole entropy computations and the AdS-CFT duality.
1 The point particle
* The bosonic point particle, the classical point particle and its Dirac quantisation, the BRST quantization of the point partic, the super point particle, the spinning particle, the Brink-Schwarz superparticle, superspace formulation of the point particle, the twistor approach to the massless point particle, twistors in four and three dimensions, the twistor point actions.
2 The classical bosonic string
* The dynamics, the closed string, the open string, the energy-momentum and angular momentum of the string, a classical solution of the open string.
3 The quantum bosonic string
* The old covariant methods, the open string, the closed string, the BRST approach, the BRST action, the world-sheet energy-momentum tensor and BRST charge, the physical state condition.
4 The light-cone approach
* The classical string in the light-cone, the quantum string in the light-cone, Lorentz symmetry, light-cone string field theory.
5 Clifford algebras and spinors
* Clifford algebras, Clifford algebras in even dimensions, spinors in even dimensions, Clifford algebras in odd dimensions, central charges, Clifford algebras in space-times of arbitrary signature.
6 The classical superstring
* The Neveu-Schwarz-Ramond (NS-R) formulation, the open superstring, the closed superstring, the Green-Schwarz formulation.
7 The quantum superstring
* The old covariant approach to the open superstring, the NS sector, the R sector, the GSO projector for the open string, the old covariant approach to the close superstring.
8 Conformal symmetry and two-dimensional field theory
* Conformal transformations, conformal transformations in D dimensions, conformal transformations in two dimensions, conformally invariant two-dimensional field theories, conformally invariant two-dimentional classical theories, conformal Ward identities, constraints due to global conformal transformations, transformations of the energy-momentum tensor, operator product expansions, commutators, descendants, states, modes, and primary fields, representations of the Virasoro algebra and minimal models.
9 Conformal symmetry and string theory
* Free field theories, the free scalar, the free fermion, first order systems, application to string theory, mapping the string to the Riemann sphere, construction of string theories, the free field representation of the minimal models.
10 String compactification and the heterotic string
* Compactification on a circle, Torus compactification, compactification in the presence of background fields, description of th emoduli space, Heterotic compactification, the heterotic string.
11 The physical states and the no-ghost theorem
* Ttheno-ghost theorem, the zero-norm physical states, the physical state projector, the cohomology of Q.
12 Gauge covariant string theory
* The problem, the solution, derivation fo the solution, the gauge covariant closed string, the gauge covariant superstring.
13 Supergravity theories in four, ten and eleven dimensions
* Four ways to construct supergravity theories, the Noether method, the on-shell superspace method, gauging of space-time groups, dimensional reduction, non-linear realisations, eleven-dimensional supergravity, the IIA supergravity theory, the IIB supergravity theory, the algebra and field content, the equations of motion, the SL.(w,R) version, symmetries of the maximal supergravitry theories in dimensions less than ten, TypeI supergravity and supersymmetric Yang-Mills theories in ten dimensions, solutions of the supergravity theories, solutions in a generic theory, brane solutions in eleven-dimensional supergravity, brandsolutions in the ten-dimensional maximal supergravity theories, brane charges and the preservation of supersymmetry.
14 Brand dynamics
* Bosonic branes, types of superbranes, simple superbranes, D-branes, branes in M theory, solutions of the 5-brand of M theory, the 3-brane, the self-dual string, five-brane dynamics and the low energy effective action of the N = 2 Yang-Mills theory.
* Bosonic D-branes, super D-branes in the NS-R formulation, D-Branes in the Green-Schwarz formulation
16 String theory and Lie algebras
* Finite dimensional and affine Lie algebras, a review of finite-dimensional Lie algebras and lattices, representations of finite dimensional semi-simple Lie algebras, Affine Liealgebras, Kac-Moody algebras, Lorentzian algebras, very extended and over-extended Lie algebras, weights and inverse Cartan matrix of E (subscript n), low level analysis of Lorentzian Kac-Moody algebras, the adjoint representations, all representations, the Kac-Moody algebra E (subscript 11), the Cartan involution invariant subalgebra of a Kac-Moody algebra, string vertex operators and Lie algebras
17 Symmetries of string theory
* T duality, electromagnetic duality, S and U duality, M theory, E theory, the eleven-dimensional theory, the IIA and IIB theories, the common origin of the eleven-dimensional IIA and IIB theories, theories in less than ten dimensions, duality symmetries and conditions, brane charges, the l (subscript 1) representation and generalised space-time, Weyl transformations of E (subscript 11) and the non-linear realisation fo its Cartan sub-algebra.
18 String interactions
* Duality, factorisation and the origins of string theory, the path integral approach, the group theoretic approach, interacting open string field theory, light-cone string field theory, mapping the interacting string, a brief discussion of interacting gauge covariant string theory.
Appendix A The Dirac and BRST methods of quantisation
Appentix B Two-dimensional light-cone and spinor conventions
Appendix C The Relationship between S (2) and the Riemann sphere
Appendix D Some properties of the classical Lie algebras
In the back matter there is an index and chapter by chapter references that the reader may wish to access for further exploration of the topic.