Normalizing flows for lattice gauge theory in arbitrary space-time dimension
This work addresses a bottleneck in high-dimensional lattice gauge theory simulations for physics researchers, representing an incremental advancement by extending existing methods to more complex geometries.
The authors tackled the challenge of applying normalizing flows to sample field configurations in lattice gauge theory beyond two dimensions, developing gauge-equivariant flow architectures that enable scalable and asymptotically exact sampling, with results demonstrated in a proof-of-principle application to SU(3) lattice gauge theory in four dimensions.
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.