Strings in Curved Spacetimes

Progress on the physics of strings in curved spacetime are comprehensively reviewed. We start by showing through renormalization group arguments that a meaningful quantum theory of gravity must be finite and must include all particle physics. Then, we review classical and quantum string propagation in curved spacetimes.We start by the general expansion method proposed by de Vega and Sánchez in 1987. The particle transmutation phenomena in asymptotically flat spacetimes are detailed including fermion-boson transitions in supergravity backgrounds. The next chapters review the exactly solvable cases of string propagation: shock waves, singular plane waves, conical spacetimes and de Sitter cosmological spacetime. The calculation of various physical quantities like the string mass and the energy-momentum tensor shows that classical and quantum string propagation in shock-waves and singular plane waves is physically meaningful and full of interesting new phenomena. The important phenomenom of string stretching that takes place when strings fall into spacetime singularities and in expanding universes is analyzed. We conclude by reporting on strings in de Sitter spacetime, where the string equations are integrable and reduce to the sinh-Gordon equation and to integrable generalizations of it. The construction of a sensible quantum theory of gravitation is probably the greatest challenge in today's theoretical physics. Deep problems arise when (second) quantization is combined with general relativity. Statistical phenomena show up (Hawking's radiation) when free fields are quantized in black-holes backgrounds. This entails a lack of quantum coherence even keeping the gravitational field classical. Another problem (the most often discussed in this connection) is the one of renormalizability of the Einstein theory (or its various generalizations) when quan-tized as a local quantum field theory. Actually, even deeper conceptual problems arise when one tries to combine quantum concepts with General Relativity. That is, it may be very well that a quantum theory of gravitation needs new concepts and ideas. Of course, this future theory must have the today's General Relativity and Quantum Mechanics (and QFT) as limiting cases. In some sense, what everybody is doing in this domain (including string theories approach) may be to the real theory what the old quantum theory in the 10's was compared with quantum mechanics. The main drawback to develop a quantum theory of gravitation is clearly the total lack of experimental guides for the theoretical developpment. Just by dimensional reasons, physical effects combining gravitation and quantum mechanics are relevant only at energies of the order of M …