Research objectives and content
The work to be developed during my stay at Department of Applied Mathematics and Theoretical Physics of the University of Cambridge deals with three related aspects of String Theory in which an application of non-perturbative string physics is still lacking.
i) The first one is the study of string thermodynamics at high temperature well string perturbation theory breaks down. The study of the string thermal ensemble from the point of view of M-theory, and in particular using its M(atrix)-theory formulation, could uncover the new physics beyond the Hagedorn temperature, where the description in terms of stringtheoretical degrees of freedom seems inadequate.
ii) The second subject included in the present proposal is to deepen the understanding of non-supersymmetric black holes from the D-brane point of view. The objective of this study will be to elucidate which are the workings behind the D- brane description of black holes and their possible extensions to more general classes of black holes that up to now cannot be microscopically described as bound states of D-branes.
iii) Finally the third part of the proposal deals with the application of non-perturbative techniques to the study of string cosmology. As it is the case with perturbative dualities and symmetries (most remarkably, T-duality), non-perturbative dualities has to play an important role in the early moments of the Universe. This study is intimately related with the possible resolution of the Hagedorn problem (see above).
These three projects are by no means disconnected, and ambitious as the research proposal may seem there are a lot o physically interesting new things to be learned from its very beginning.
Training content (objective, benefit and expected impact)
The High Energy Physics group at DAMTP is one of the leading groups in the world in the study of non-perturbative aspec of String Theory. In carrying out the outlined research proposal there I will have the unique opportunity of working contact with the physicists that are leading the field, with the obvious benefit of not only learn new techniques firsthand, b also of having the possibility of establishing collaborations with my colleagues at DAMTP as well as at Physics Departmer of other Universities in the United Kingdom with whom the DAMTP has close scientific relations. I firmly think that t possibility of working for two years at the University of Cambridge will be crucial for my training as a theoretical physi and will determine in a very positive way my future contributions to the field.