Mathematics Colloquia and Seminars

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Recent interest in tensor network models has led to speculation that such networks provide a natural discretization of the AdS/CFT correspondence. This raises many questions: just to begin, is there any sort of lattice field theory model underlying this connection? And how much of the usual AdS/CFT dictionary can really be said to make sense in a discrete setting? I'll describe some recent work that proposes a setting in which such questions can perhaps be addressed: a discrete spacetime in which a group of isometries act, in a sense, by conformal transformations on the boundary. Many of the basic first steps in the AdS/CFT dictionary carry over without much alteration to lattice field theories in this background, and one can even consider natural analogues of BTZ black hole geometries. The class of boundary theories that appear in this context are interesting in their own right, and are analogues of hierarchical models studied by Dyson and many others; given time, I'll discuss some such interacting theories of both bosons and fermions.