arXiv:2305.02402·v1·High Energy Physics — Lattice
Normalizing flows for lattice gauge theory in arbitrary space-time dimension
Ryan Abbott🇺🇸 · Michael S. Albergo🇺🇸 · Aleksandar Botev🇬🇧 · Denis Boyda🇺🇸 · Kyle Cranmer🇺🇸 · Daniel C. Hackett🇺🇸 · Gurtej Kanwar🇺🇸 · Alexander G.D.G. Matthews🇬🇧 · Sébastien Racanière🇬🇧 · Ali Razavi🇬🇧 · Danilo J. Rezende🇬🇧 · Fernando Romero-López🇺🇸 · Phiala E. Shanahan🇺🇸 · Julian M. Urban🇺🇸
Abstract
Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow architectures facilitating the generalization to higher-dimensional lattice geometries. Specifically, we discuss masked autoregressive transformations with tractable and unbiased Jacobian determinants, a key ingredient for scalable and asymptotically exact flow-based sampling algorithms. For concreteness, results from a proof-of-principle application to SU(3) lattice gauge theory in four space-time dimensions are reported.