Relativistic extended objects and their gravitational and gauge interactions Dr. Euro SPALLUCCI Researcher Prof. Franco LEGOVINI Associate Professor Dr. Stefano ANSOLDI Research assistant Yang-Mills theories and extended objects Yang-Mills theories play a central role in the formulation of fundamental interactions. In this framework the theory of gravitation is still in an unclear position: in particular a consistent quantum theory of gravity requires the presence of extended objects not only as fundamental constituents of the matter content in our universe, but also as building blocks of the intrinsic structure of spacetime. Of course the validity of this point of view will be confirmed only if it will be possible to recover, in the low energy-limit, the usual predominant role of gauge theories. In an unified scheme, as the one furnished by M-theory, for instance, it is thus crucial to establish a relation between extended objects and Yang-Mills fields: for this reason the corrispondence between string theory and gauge theory, already established in the large-N limit, are to be extended also to higher dimensional objects that can be found in the spectrum of M-theory. In particular, it is certainly crucial to find a closer relation between extended objects and QCD. A first step in this direction has already been taken with the proof that a four dimensional Yang-Mills theory with a topological term can be be related in the quenching and large-N approximations to the model containing an open 3-brane, whose interior can be identified with an hadronic bag. Then, the next step consists in extending this correspondence to higher dimensional objects in more than four dimensions: for instance it is possible to consider a generalized, reduced, quenched Yang-Mills theory in 4k-dimensions and to use a Weyl-Wigner-Moyal mapping to identify it with a field theory in a non'commutative space. This could lead to interesting connections between the low energy limit of a theory with extended objects (which naturally describes gravity) and gauge theories. Morover it could also be a starting point for a deeper connection between quantum gravity and theories defined in non-commutative spaces, which could play a primary role in process pertaining to the Planck scale domain. In this direction results concerning non-commutative harmonic oscillators have already been obtained. Non-perturbative quantization of relativistic extended objects In the framework of the path-integral quantization of a bosonic p-brane we have extended to the semiclassical level the equivalence between diverse classical actions. In more detail, we have considered a p-brane model in which the 'tension' is not a pre-assigned parameter, but is induced from the dynamics of a p-gauge form. In the classical realm this model is equivalent to a Nambu-Goto/Howe-Tucker model, and we extended this equivalence at the path-integral level using the WKB approximation: the gauge part of the model has been studied in a 'first order formalism' by the introduction of a new 'reduced procedure' of quantization a la Fadeev-Popov. This result suggests that both, at the classical as well as the quantum level, a new principle of unification (or universality) could be at work; although it is still unknown, it seems that thanks to it the p-brane dynamics results independent, to a large extent, from the model chosen for the action principle. Dynamics of extended objects in General Relativity The analysis of the dynamics of extended objects in General Relativity using Israel's junction conditions has often been used in the past to obtain tractable models of complex gravitational systems, especially in connection with the long-standing problem of gravitational collapse. Nowadays the relevance of the model is connected with the analysis of systems in which quantum gravitational effects should be the most relevant ones. Keeping an eye to more general problems, especially connected with black hole entropy, black hole thermodynamics and the relevance of information theory for quantum gravity, we studied the quantum states of general relativistic shells in the semiclassical approximation. INTERNATIONAL COLLABORATIONS: prof. Werner Israel, University of Victoria (Canada), prof. Antonio Aurilia, California State Polytechnic University (USA), prof. Eduardo I.Guendelman, Ben Gurion University (Israel)

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