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Title:
Curved Lattice Field Theory for CFT Data
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Abstract:
Curved manifolds provide a natural arena for studying nonperturbative conformal fixed points. On S^d critical theories have no finite volume effects, and on RxS^{d-1} critical theories have finite correlation lengths related directly to the CFT scaling dimensions. We review the quantum finite element (QFE) scheme, which provides a nonperturbative lattice regularization for renormalizable QFT on a smooth Riemannian manifold. Numerical results for \phi^4 theory on S^2 and RxS^2 -- whose critical behaviors are governed by the 2- and 3-d Ising CFTs respectively -- will be discussed. We will remark on ongoing efforts to simulate finite density systems in radial quantization.
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