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Equivariant Flow-Based Sampling for Lattice Gauge Theory.

Gurtej Kanwar1, Michael S Albergo2, Denis Boyda1

  • 1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

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|October 5, 2020
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Summary
This summary is machine-generated.

We developed new gauge-invariant machine-learning algorithms for lattice gauge theories. These algorithms significantly outperform traditional methods for sampling topological quantities in U(1) gauge theory.

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Area of Science:

  • Computational physics
  • High energy physics
  • Machine learning

Background:

  • Lattice gauge theories are fundamental in quantum field theory.
  • Traditional sampling methods like hybrid Monte Carlo can be inefficient.
  • Gauge invariance is crucial for physical predictions in lattice gauge theories.

Purpose of the Study:

  • To introduce a novel class of machine-learned flow-based sampling algorithms for lattice gauge theories.
  • To ensure these algorithms are inherently gauge invariant.
  • To test the efficiency of this framework on a specific U(1) gauge theory model.

Main Methods:

  • Development of gauge-invariant flow-based generative models.
  • Application to U(1) lattice gauge theory in two spacetime dimensions.
  • Comparison with traditional hybrid Monte Carlo and heat bath algorithms.

Main Results:

  • The proposed machine-learned algorithms are gauge invariant by construction.
  • For U(1) gauge theory at small bare coupling, the new method is orders of magnitude more efficient.
  • Efficient sampling of topological quantities was achieved.

Conclusions:

  • Machine-learned flow-based sampling offers a powerful and efficient alternative for lattice gauge theories.
  • The gauge-invariant construction ensures physical relevance.
  • This framework shows significant promise for advancing computational studies in quantum field theory.