Entanglement Entropy in 2D Non-abelian Pure Gauge Theory

Abstract

We compute the Entanglement Entropy (EE) of a bipartition in 2D pure non-abelian $U(N)$ gauge theory. We obtain a general expression for EE on an arbitrary Riemann surface. We find that due to area-preserving diffeomorphism symmetry EE does not depend on the size of the subsystem, but only on the number of disjoint intervals defining the bipartition. In the strong coupling limit on a torus we find that the scaling of the EE at small temperature is given by $S(T)-S(0)=O\left(\frac{m_{gap}}{T}{e}^{-\frac{m_{gap}}{T}}\right)$, which is similar to the scaling for the matter fields recently derived in literature. In the large $N$ limit we compute all of the Renyi entropies and identify the Douglas-Kazakov phase transition.

arXiv comment6 pages

References in corpus (24)

• Entanglement Entropy and Quantum Field Theory
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Symmetry protected topological orders and the group cohomology of their symmetry group
• On Geometric Entropy
• Entanglement as a Probe of Confinement
• Two Dimensional QCD is a String Theory
• Remarks on entanglement entropy for gauge fields
• Black Hole Entropy and Entropy of Entanglement
• Large $N$ Phase Transition in Continuum QCD${}_2$
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
• Decomposition of entanglement entropy in lattice gauge theory
• Entanglement entropy in gauge theories and the holographic principle for electric strings
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
• Entanglement Entropy of a Massive Fermion on a Torus
• Do gauge fields really contribute negatively to black hole entropy?
• Entanglement entropy in d+1 SU(N) gauge theory
• Large-N quantum gauge theories in two dimensions
• Geometric Entropy and Hagedorn/Deconfinement Transition
• Tracing Through Scalar Entanglement

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• Entanglement branes, modular flow, and extended topological quantum field theory
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• $T\overline{T}$-deformation of $q$-Yang-Mills theory
• Strong Coupling Expansion of the Entanglement Entropy of Yang-Mills Gauge Theories
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• Entanglement entropy and the large $N$ expansion of two-dimensional Yang-Mills theory
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• Entanglement Entropy and Duality
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