Tensor networks, p-adic fields, and algebraic curves: arithmetic and the AdS3 / CFT2 correspondence - Heydeman, Matthew; Marcolli, Matilde; Saberi, Ingmar; Stoica, Bogdan (Advances in theoretical and mathematical physics, 2018)
One of the many remarkable properties of conformal field theory in two dimensions is its connection to algebraic geometry. Since every compact Riemann surface is a projective algebraic curve, many constructions of interest in physics (which a priori depend on the analytic structure of the spacetime) can be formulated in purely algebraic language. This opens the door to interesting generalizations, obtained by taking another choice of field: for instance, the p-adics. We generalize the AdS/CFT correspondence according to this principle; the result is a formulation of holography in which the bulk geometry is discrete—the Bruhat–Tits tree for PGL(2,Qp)—but the group of bulk isometries nonetheless agrees with that of boundary conformal transformations and is not broken by discretization.