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Entanglement entropy in Abelian gauge theories

P. V. Buividovich, M.I. Polikarpov

The definition of geometric entanglement entropy associated with some region in space is discussed for the case of gauge theories. It is argued that since in gauge theories elementary excitations look like loops (closed electric strings) rather than points (particles), the boundaries of the regions should also carry some nonzero entropy. This entropy counts the number of strings which cross these boundaries. Explicit calculations of such entropy are carried out in the limits of infinitely strong and weak couplings of three- and four-dimensional Z N gauge theories. In three dimensions we find that the entropy is a constant which does not depend on the region, while in four dimensions the familiar area law for the entropy is recovered.The definition of geometric entanglement entropy associated with some region in space is discussed for the case of gauge theories. It is argued that since in gauge theories elementary excitations look like loops (closed electric strings) rather than points (particles), the boundaries of the regions should also carry some nonzero entropy. This entropy counts the number of strings which cross these boundaries. Explicit calculations of such entropy are carried out in the limits of infinitely strong and weak couplings of three- and four-dimensional Z N gauge theories. In three dimensions we find that the entropy is a constant which does not depend on the region, while in four dimensions the familiar area law for the entropy is recovered.

Physics of Atomic NucleiSep 1, 20091 citation

Entanglement Entropy and Entanglement Growth in Gauge Theory

Naoki Watamura, 尚毅綿村

Mar 26, 20180 citations

Entanglement and thermal entropy of gauge fields

Christopher Eling, Yaron Oz, Stefan Theisen

arXiv:1308.4964Journal of High Energy PhysicsNov 1, 201327 citations

Roughening and dynamics of an electric flux string in a (2+1)D lattice gauge theory

Francesco Di Marcantonio, Sunny Pradhan, Sofia Vallecorsa +2 more

The roughening transition in Z2 lattice gauge theory remains a complex phenomenon, particularly in understanding the behavior of electric flux strings. Here, the authors use numerical simulations with matrix product states to reveal the universal Lüscher correction and distinct entanglement entropy growth, offering insights into string dynamics and symmetry restoration near deconfinement.

arXiv:2505.23853Communications PhysicsMay 17, 20263 citations

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

William Donnelly, Sydney Timmerman, Nicolás Valdés-Meller

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,” − Σ 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.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,” − Σ 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:1911.09302Journal of High Energy PhysicsApr 1, 202018 citations

Aspects of holographic entanglement entropy

Shinsei Ryu, Tadashi Takayanagi

arXiv:hep-th/0605073Journal of High Energy PhysicsAug 21, 20061,962 citations

Entanglement entropy in gauge theories and the holographic principle for electric strings

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