Speaker
Prof.
Richard C. Brower
(Boston University)
Description
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)