Prospects for Lattice QFTs on Curved Riemann Manifolds

Authors

Richard C. Brower, Boston University
Casey E. Berger, Smith CollegeFollow
George T. Fleming, Yale University
Andrew D. Gasbarro, University of Bern
Evan K. Owen, Boston University
Timothy G. Raben, Michigan State University
Chung I. Tan, Brown University
Evan S. Weinberg, NVIDIA

Document Type

Conference Proceeding

Publication Date

7-8-2022

Publication Title

Proceedings of Science

Abstract

Conformal or near conformal Quantum Field Theories QFT) would benefit from a rigorous non-perturbative lattice formulation beyond the flat Euclidean space, Rd. Although all UV complete QFT are generally acknowledged to be perturbatively renormalizable on smooth Riemann manifolds, non-perturbative realization on simplicial lattices (triangulation) encounter difficulties as the UV cut-off is removed. We review the Quantum Finite Element (QFE) method that combines classical Finite Element with new quantum counter terms designed to address this. The construction for maximally symmetric spaces (Sd, R × Sd−1 and AdSd+1) is outlined with numerical tests on R × S2 and a description of theoretical and algorithmic challenges for d = 3, 4 QFTs.

Volume

396

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Rights

© Copyright owned by the author(s)

Comments

Archived as published.

Recommended Citation

Brower, Richard C.; Berger, Casey E.; Fleming, George T.; Gasbarro, Andrew D.; Owen, Evan K.; Raben, Timothy G.; Tan, Chung I.; and Weinberg, Evan S., "Prospects for Lattice QFTs on Curved Riemann Manifolds" (2022). Physics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/phy_facpubs/98