Abstract
We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic order parameter associated with charged operators in the thermofield double state, was proven in a previous article by Casini, Huerta, Pontello, and the present author. Here we describe how the statement about the entropic order parameter arises, and how it gets transformed into the universal density of states. The use of the certainty principle, relating the entropic order and disorder parameters, is crucial for the proof. We remark that although the immediate application of this result concerns charged states, the origin and physics of such density can be understood by looking at the vacuum sector only. We also describe how these arguments lie at the origin of the so-called entropy equipartition in these type of systems, and how they generalize to QFT’s on non-compact manifolds.
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H. Casini, M. Huerta, J. M. Magán and D. Pontello, Entanglement entropy and superselection sectors. Part I. Global symmetries, JHEP 02 (2020) 014 [arXiv:1905.10487] [INSPIRE].
J. M. Magán and D. Pontello, Quantum Complementarity through Entropic Certainty Principles, Phys. Rev. A 103 (2021) 012211 [arXiv:2005.01760] [INSPIRE].
H. Casini, M. Huerta, J. M. Magán and D. Pontello, Entropic order parameters for the phases of QFT, JHEP 04 (2021) 277 [arXiv:2008.11748] [INSPIRE].
H. Casini and J. M. Magán, On completeness and generalized symmetries in quantum field theory, to appear in Mod. Phys. Lett. A, arXiv:2110.11358 [INSPIRE].
D. Harlow and H. Ooguri, A universal formula for the density of states in theories with finite-group symmetry, arXiv:2109.03838 [INSPIRE].
J. C. Xavier, F. C. Alcaraz and G. Sierra, Equipartition of the entanglement entropy, Phys. Rev. B 98 (2018) 041106 [arXiv:1804.06357] [INSPIRE].
S. Murciano, G. Di Giulio and P. Calabrese, Entanglement and symmetry resolution in two dimensional free quantum field theories, JHEP 08 (2020) 073 [arXiv:2006.09069] [INSPIRE].
A. Milekhin and A. Tajdini, Charge fluctuation entropy of Hawking radiation: a replica-free way to find large entropy, arXiv:2109.03841 [INSPIRE].
S. Pal and Z. Sun, High Energy Modular Bootstrap, Global Symmetries and Defects, JHEP 08 (2020) 064 [arXiv:2004.12557] [INSPIRE].
S. Doplicher, R. Haag and J. E. Roberts, Fields, observables and gauge transformations I, Commun. Math. Phys. 13 (1969) 1 [INSPIRE].
S. Doplicher, R. Haag and J. E. Roberts, Fields, observables and gauge transformations II, Commun. Math. Phys. 15 (1969) 173 [INSPIRE].
S. Doplicher, R. Haag and J. E. Roberts, Local observables and particle statistics. 1, Commun. Math. Phys. 23 (1971) 199 [INSPIRE].
S. Doplicher, R. Haag and J. E. Roberts, Local observables and particle statistics. 2, Commun. Math. Phys. 35 (1974) 49 [INSPIRE].
R. Longo, Index of subfactors and statistics of quantum fields. I, Commun. Math. Phys. 126 (1989) 217 [INSPIRE].
R. Longo and K.-H. Rehren, Nets of subfactors, Rev. Math. Phys. 7 (1995) 567 [hep-th/9411077] [INSPIRE].
D. Petz, Quantum information theory and quantum statistics, Springer Science & Business Media (2007).
M. Ohya and D. Petz, Quantum entropy and its use, Springer Science & Business Media (2004).
V. Jones, Index for subfactors, Invent. Math. 72 (1983) 1 and online at http://eudml.org/doc/143011.
H. Kosaki, Extension of Jones’ theory on index to arbitrary factors, J. Funct. Anal. 66 (1986) 123.
Y. Kawahigashi, R. Longo and M. Müger, Multiinterval subfactors and modularity of representations in conformal field theory, Commun. Math. Phys. 219 (2001) 631 [math/9903104] [INSPIRE].
T. Teruya, Index for von Neumann algebras with finite-dimensional centers, Publ. Res. Inst. Math. Sci. 28 (1992) 437.
S. Hollands, Variational approach to relative entropies (with application to QFT), Lett. Math. Phys. 111 (2021) 136 [arXiv:2009.05024] [INSPIRE].
S. Doplicher and J. E. Roberts, Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics, Commun. Math. Phys. 131 (1990) 51 [INSPIRE].
A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321 (2006) 2.
R. Haag, Local quantum physics: Fields, particles, algebras, Springer Science & Business Media (2012).
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Magán, J.M. Proof of the universal density of charged states in QFT. J. High Energ. Phys. 2021, 100 (2021). https://doi.org/10.1007/JHEP12(2021)100
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DOI: https://doi.org/10.1007/JHEP12(2021)100