An Invitation to String Theory

These lectures are supposed to give a point of entry into that vast web of related ideas that go under the name “string theory”. I start with a more or less qualitative introduction to gravity as a field theory and sketch how one might try to quantize it. Quantizing gravity using the usual techniques of field theory will turn out to be unsuccessful, and that will be a motivation for trying an indirect approach: string theory. I present bosonic string theory, quantize the closed string in the light cone gauge and show that one of the states in the closed string Hilbert space can be interpreted as a graviton. I will end with some general qualitative ideas on slightly more advanced topics. 1 Gravity and the Necessity for String Theory I want to thank Prof. Sathish for giving me a chance to speak here about string theory. I hope I can rise to the expectations that might have been generated by his extremely kind and generous introduction. The aim of the organizers to expose the students to topics beyond curricula is truly laudable. Often, the inspiration for trudging through a lot of what goes for as “syllabus” is to be found in what lies beyond it. By giving the impression that whatever that is worth doing has already been done, and by making it seem that the people who make contributions in physics are larger than life (and often belong to a different place, time and race), the educational system fails to impart the most important ingredient that a theoretical physicist needs: the confidence to write down an equation. The remedy for this, I believe, is to not present physics as a completed business, and to expose the inadequacies and failings of our present world-view. That way, it becomes clear that there are many profound questions which have remained unanswered despite the work of many great people. String theory is necessary because we don’t know of any other way in which to make a theory of gravity that doesn’t contradict Quantum Mechanics. To me, this is the most compelling, indeed irresistible, reason for liking string theory. There is not a single experiment or observation that violates the principles of QM, and so the construction of a Quantum theory of Gravity is a necessity, not an option: and this is precisely what string theory claims to provide. There are some other reasons for liking string theory all of them impressive: string theory manages, at least at a schematic level, to unify all the forces (gravity being just one of the four) in nature. Also we believe that string theory is an absolutely unique theory we cannot tweak the parameters in the theory to make it do what we want; changing things capriciously will make it mathematically inconsistent. But I feel that these reasons are secondary and more aesthetic. If the forces in nature are unified, thats nice and pretty, but we have no fully compelling a priori reason for believing that the forces have to be unified. And again, uniqueness is wonderful and we would expect that from a final theory, but how do we know that there is a final theory? For my part, I do think that there is one, but I do not know of a watertight argument that would convince a skeptic. The theory of gravity that we know and love is Einstein’s GR. It has certain problems of its own, like the existence of singularities regions of spacetime where the theory breaks down. A theory that fails at certain limits of its range of applicability is not what we would call a complete theory. Usually singularities arise because of the infinite resolution that a manifold There seems to be some confusion among the students about unification: Grand Unified Theories (GUTs) are theories that unify all the forces EXCEPT gravity they are not so grand in that sense. But string theory claims to go beyond that and includes gravity as well. GUTs are specific quantum field theories, just like QED or scalar field theory, but string theory is much more than a QFT.