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Discrete two-dimensional quantum gravity and large n field theories


One of the most exciting developments in the world of theoretical physics in recent years has been the discovery of exact solutions to discrete models of closed string theory. The methods developed use a correspondence between the discretised string world sheet and the 1/N expansion of field theoretic models of NxN matrices.
These results have had a profound impact in the domain of string theory models. For realistic string theories, however, solutions will have to be found for matter fields (target spaces) with dimensions D=C>1. This is one of the directions envisaged for the proposed research.
In addition, there exist many intriguing relations in two dimensional physics between matter fields with and without gravitational coupling. This presents an opportunity to unify two dimensional physics through interpolating models connecting gravitational and flat phases of the same matter fields. This forms the second aim of proposed research.

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