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Abstract: The concept of a -space of quantum field theories- or -theory space- was setout in the 1970-s in work of Wilson, Friedan and others. This structure shouldplay an important role in organizing and classifying QFTs, and in the study ofthe string landscape, allowing us to say when two theories are connected byfinite variations of the couplings or by RG flows, when a sequence of QFTsconverges to another QFT, and bounding the amount of information needed touniquely specify a QFT, enabling us to estimate their number. As yet we do nothave any definition of theory space which can be used to make such arguments.In this talk, we will describe various concepts and tools which should bedeveloped for this purpose, inspired by the analogous mathematical problem ofstudying the space of Riemannian manifolds. We state two general conjecturesabout the space of two-dimensional conformal field theories, and we define adistance function on this space, which gives a distance between any pair oftheories, whether or not they are connected by varying moduli.Based on talks given at QTS6 University of Kentucky, Erice, Texas Aand M, andNorthwestern University. To appear in the proceedings of QTS6.

Autor: Michael R. Douglas


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