Symmetric gauge theories and Lieb-Schultz-Mattis-type constraints

Dominic V. Else, Ryan Thorngren

Ryohei Kobayashi, Ken Shiozaki, Yuta Kikuchi +1 more

The authors construct a Lieb-Schultz-Mattis (LSM)-type theorem applicable for abelian gauge theories without matter. This theorem is based on generalized global symmetries acting on Wilson lines. It provides strong constraints on possible phases, realized in lattice gauge theories. The generalized LSM theorem is demonstrated on the example of a U(1) gauge theory that simulates the quantum dimer model on a bipartite lattice. The authors find a mixed `t Hooft anomaly involving the generalized global symmetry at the Rokhsar-Kivelson critical point that corresponds to the LSM constraint.

Richard Healey

Andrew Stewart Caldin

FINDING: Higher-rank symmetric tensor gauge theories impose lattice symmetry constraints analogous to Lieb-Schultz-Mattis (LSM) theorems, linking topological order to lattice geometry. | MATH: LSM-type constraints relate filling fraction ν to lattice translation symmetry: ν × (unit cell area) must be integer for gapped phases without fractionalization. In higher-rank theories, gauge fields are symmetric tensors (e.g., A_{ij} = A_{ji}) with Gauss law: ∂_i ∂_j E^{ij} = ρ. Lattice symmetries enforce quantization of gauge charge and flux. | CONNECTION: Crystallographic symmetries (e.g., square, triangular, honeycomb lattices) dictate allowed tensor ranks and commutation relations. Root systems (A_n, B_n, etc.) appear in multipole algebras. No direct ratios (0.618, 1.618) found. Base-60 not present. | DEPTH: 7 — Bridges topological field theory with discrete lattice constraints, revealing how continuum geometric symmetries emerge from lattice data. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Gabriel Catren

F.A. Bais, Peter van Driel, Mark de Wild Propitius