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Compact U^{k}(1) Chern-Simons Theory as a Local Bosonic Lattice Model with Exact Discrete 1-Symmetries.

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We developed a lattice model for a U(1) rotor, matching Chern-Simons theory low-energy properties. This model reveals quantized matrices and anomalous symmetries, crucial for understanding topological field theories.

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Area of Science:

  • Condensed Matter Physics
  • High Energy Physics
  • Lattice Field Theory

Background:

  • Chern-Simons theory describes topological phases of matter.
  • Lattice models are essential for non-perturbative quantum field theory studies.
  • Understanding symmetries and anomalies is key to classifying topological phases.

Purpose of the Study:

  • To propose a novel bosonic U(1) rotor model on a 3D spacetime lattice.
  • To demonstrate the semiclassical validity of the model for low-energy properties.
  • To connect lattice model features to Chern-Simons field theory.

Main Methods:

  • Construction of a bosonic U(1) rotor model on a 3D spacetime lattice.
  • Inclusion of a Maxwell term to study low-energy dynamics.
  • Application of a semiclassical approach for property extraction.
  • Analysis of compact lattice variables and their implications for matrix quantization.
  • Investigation of lattice 1-form symmetries and their anomalies.

Main Results:

  • The low-energy properties of the lattice model reproduce those of Chern-Simons field theory.
  • Compact lattice variables enforce quantization of the K matrix (symmetric, integer, even diagonals).
  • The model exhibits exact 1-form symmetries, including anomalous ones, consistent with Chern-Simons theory.
  • Anomalies are observable through symmetry breaking at lattice boundaries.

Conclusions:

  • The proposed lattice rotor model provides a viable non-perturbative approach to studying Chern-Simons field theory.
  • The model successfully captures essential features like quantized topological terms and anomalous symmetries.
  • Boundary effects offer a method to probe and understand these anomalies within the lattice framework.