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Correlation decay for finite lattice gauge theories at weak coupling

Arka Adhikari, Sky Cao

Abstract

In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables.

Correlation decay for finite lattice gauge theories at weak coupling

Abstract

In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables.
Paper Structure (22 sections, 39 theorems, 131 equations, 1 figure)

This paper contains 22 sections, 39 theorems, 131 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Previous work
  3. The difference between finite Abelian and finite non-Abelian
  4. Definitions and Notation
  5. Acknowledgements
  6. Preliminaries
  7. A general swapping argument
  8. Knot decomposition
  9. Construction of the swapping map
  10. Probability bound
  11. Topological facts
  12. Edge configurations and homomorphisms
  13. Good rectangles
  14. Knot upper bound
  15. Higgs Boson Large k
  16. ...and 7 more sections

Key Result

Theorem 1.1

Let $\beta \geq \frac{1}{\Delta_G}(114 + 4 \log |G|)$. Let $L \geq 0$. Let $B_1, B_2 \subseteq \Lambda$ be rectangles that are at a $\ell^\infty$ distance at least $L$ from each other (i.e., the $\ell^\infty$ distance between any vertex $x$ of $B_1$ and any vertex $y$ of $B_2$ is at least $L$). Let

Figures (1)

  • Figure 1:

Theorems & Definitions (98)

  • Theorem 1.1
  • Remark 1.2
  • Definition 2.1
  • Remark 2.2
  • Lemma 2.3
  • Lemma 2.4
  • Remark 2.5
  • Definition 2.6
  • Definition 2.7
  • Lemma 2.8
  • ...and 88 more