Entanglement entropy and the large $N$ expansion of two-dimensional Yang-Mills theory

Abstract

Two-dimensional Yang-Mills theory is a useful model of an exactly solvable gauge theory with a string theory dual at large $N$. We calculate entanglement entropy in the $1/N$ expansion by mapping the theory to a system of $N$ fermions interacting via a repulsive entropic force. The entropy is a sum of two terms: the "Boltzmann entropy", $\log \dim (R)$ per point of the entangling surface, which counts the number of distinct microstates, and the "Shannon entropy", $-\sum p_R\log p_R$, which captures fluctuations of the macroscopic state. We find that the entropy scales as $N^2$ in the large $N$ limit, and that at this order only the Boltzmann entropy contributes. We further show that the Shannon entropy scales linearly with $N$, and confirm this behaviour with numerical simulations. While the term of order $N$ is surprising from the point of view of the string dual - in which only even powers of $N$ appear in the partition function - we trace it to a breakdown of large $N$ counting caused by the replica trick. This mechanism could lead to corrections to holographic entanglement entropy larger than expected from semiclassical field theory.

arXiv comment31 pages, 8 figures

References in corpus (32)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entropy and Area
• A Covariant Holographic Entanglement Entropy Proposal
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Quantum corrections to holographic entanglement entropy
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
• The Page curve of Hawking radiation from semiclassical geometry
• Two Dimensional Gauge Theories Revisited
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Local subsystems in gauge theory and gravity
• Two Dimensional QCD is a String Theory
• Large $N$ Phase Transition in Continuum QCD${}_2$
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• Two Dimensional QCD as a String Theory
• Entanglement entropy in gauge theories and the holographic principle for electric strings
• Twists and Wilson Loops in the String Theory of Two Dimensional QCD
• Entanglement entropy and nonabelian gauge symmetry
• Aspects of Entanglement Entropy for Gauge Theories
• Instanton Induced Large $N$ Phase Transitions in Two and Four Dimensional QCD
• Equivalence of Two Dimensional QCD and the $c=1$ Matrix Model
• Strings on a Cone and Black Hole Entropy
• Entanglement entropy in two dimensional string theory
• Renormalization of Entanglement Entropy and the Gravitational Effective Action
• Coarse-grained entropy and causal holographic information in AdS/CFT
• Open Strings On The Rindler Horizon
• Entanglement branes in a two-dimensional string theory
• Mutual information challenges entropy bounds
• Entanglement Entropy in 2D Non-abelian Pure Gauge Theory
• Two-dimensional Yang-Mills Theories Are String Theories
• Entanglement branes, modular flow, and extended topological quantum field theory
• Resurgence analysis of 2d Yang-Mills theory on a torus
• Topological string entanglement

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