Abstract
Quantum field theory defined on a noncommutative space is a useful toy model of quantum gravity and is known to have several intriguing properties, such as nonlocality and UV/IR mixing. They suggest novel types of correlation among the degrees of freedom of different energy scales. In this paper, we investigate such correlations by the use of entanglement entropy in the momentum space. We explicitly evaluate the entanglement entropy of scalar field theory on a fuzzy sphere and find that it exhibits different behaviors from that on the usual continuous sphere. We argue that these differences would originate in different characteristics; non-planar contributions and matrix regularizations. It is also found that the mutual information between the low and the high momentum modes shows different scaling behaviors when the effect of a cutoff becomes important.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].
S. Minwalla, M. Van Raamsdonk and N. Seiberg, Noncommutative perturbative dynamics, JHEP 02 (2000) 020 [hep-th/9912072] [INSPIRE].
V. Balasubramanian, M. B. McDermott and M. Van Raamsdonk, Momentum-space entanglement and renormalization in quantum field theory, Phys. Rev. D 86 (2012) 045014 [arXiv:1108.3568] [INSPIRE].
J. Madore, The Fuzzy sphere, Class. Quant. Grav. 9 (1992) 69 [INSPIRE].
C.-S. Chu, J. Madore and H. Steinacker, Scaling limits of the fuzzy sphere at one loop, JHEP 08 (2001) 038 [hep-th/0106205] [INSPIRE].
S. Kawamoto, T. Kuroki and D. Tomino, Renormalization group approach to matrix models via noncommutative space, JHEP 08 (2012) 168 [arXiv:1206.0574] [INSPIRE].
S. Kawamoto and T. Kuroki, Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models, JHEP 06 (2015) 062 [arXiv:1503.08411] [INSPIRE].
S. Okuno, M. Suzuki and A. Tsuchiya, Entanglement entropy in scalar field theory on the fuzzy sphere, Prog. Theor. Exp. Phys. 2016 (2016) 023B03 [arXiv:1512.06484] [INSPIRE].
M. Suzuki and A. Tsuchiya, A generalized volume law for entanglement entropy on the fuzzy sphere, Prog. Theor. Exp. Phys. 2017 (2017) 043B07 [arXiv:1611.06336] [INSPIRE].
S. Kawamoto and T. Kuroki, work in progress.
D. A. Varshalovich, A. N. Moskalev and V. K. Khersonsky, Quantum Theory Of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols, World Scientific, Singapore (1988).
F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. Clark eds., NIST Handbook of Mathematical Functions, Cambridge University Press, Cambridge U.K. (2010) and online at https://dlmf.nist.gov/.
J. L. F. Barbón and C. A. Fuertes, Holographic entanglement entropy probes (non)locality, JHEP 04 (2008) 096 [arXiv:0803.1928] [INSPIRE].
W. Fischler, A. Kundu and S. Kundu, Holographic Entanglement in a Noncommutative Gauge Theory, JHEP 01 (2014) 137 [arXiv:1307.2932] [INSPIRE].
J. L. Karczmarek and C. Rabideau, Holographic entanglement entropy in nonlocal theories, JHEP 10 (2013) 078 [arXiv:1307.3517] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
N. Shiba and T. Takayanagi, Volume Law for the Entanglement Entropy in Non-local QFTs, JHEP 02 (2014) 033 [arXiv:1311.1643] [INSPIRE].
J. L. Karczmarek and P. Sabella-Garnier, Entanglement entropy on the fuzzy sphere, JHEP 03 (2014) 129 [arXiv:1310.8345] [INSPIRE].
F. A. Smirnov and A. B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
A. Cavaglià, S. Negro, I. M. Szécsényi and R. Tateo, \( T\overline{T} \)-deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2107.08907
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kawamoto, S., Kuroki, T. Momentum-space entanglement in scalar field theory on fuzzy spheres. J. High Energ. Phys. 2021, 101 (2021). https://doi.org/10.1007/JHEP12(2021)101
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2021)101