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22-28 July 2018
Kellogg Hotel and Conference Center
EST timezone

Prospects for Lattice QFTs on Curved Riemann Manifolds

Jul 26, 2018, 11:20 AM
Big Ten A (Kellogg Hotel and Conference Center)

Big Ten A

Kellogg Hotel and Conference Center

219 S Harrison Rd, East Lansing, MI 48824
Theoretical Developments Theoretical Developments


Prof. Richard C. Brower (Boston University)


Conformal or near conformal QFTs would benefit from a rigorous non-perturbative lattice formulation beyond the flat Euclidean space, $\mathbb R^d.\;$ Although all UV complete QFT are known to be also perturbatively renormalizable on any smooth Riemann manifold, non-perturbative realization on simplicial lattices (triangulations) encounter difficulties as the UV cut-off isremoved. We review the Quantum Finite Element (QFE) method that combines classical Finite Element and Regge Geometry with new quantum counter terms designed to address this. The construction for maximally symmetric spaces $(\mathbb S^d, \mathbb R \times \mathbb S^{d-1}$ and $\mathbb Ad{\mathbb S}^{d+1})$ is outlined with numerical tests on $\mathbb S^2$ and a description of theoretical and algorithmic challenges for $d = 3, 4$ QFTs.

Primary author

Prof. Richard C. Brower (Boston University)

Presentation Materials