Abstract
We study the properties of pseudo entropy, a new generalization of entanglement entropy, in free Maxwell field theory in d = 4 dimension. We prepare excited states by the different components of the field strengths located at different Euclidean times acting on the vacuum. We compute the difference between the pseudo Rényi entropy and the Rényi entropy of the ground state and observe that the difference changes significantly near the boundary of the subsystems and vanishes far away from the boundary. Near the boundary of the subsystems, the difference between pseudo Rényi entropy and Rényi entropy of the ground state depends on the ratio of the two Euclidean times where the operators are kept. To begin with, we develop the method to evaluate pseudo entropy of conformal scalar field in d = 4 dimension. We prepare two states by two operators with fixed conformal weight acting on the vacuum and observe that the difference between pseudo Rényi entropy and ground state Rényi entropy changes only near the boundary of the subsystems. We also show that a suitable analytical continuation of pseudo Rényi entropy leads to the evaluation of real-time evolution of Rényi entropy during quenches.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.L. Cardy and I. Peschel, Finite Size Dependence of the Free Energy in Two-dimensional Critical Systems, Nucl. Phys. B 300 (1988) 377 [INSPIRE].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
P. Calabrese and J. Cardy, Entanglement entropy and conformal field theory, J. Phys. A 42 (2009) 504005 [arXiv:0905.4013] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
V.E. Hubeny, M. Rangamani, and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
Y. Nakata, T. Takayanagi, Y. Taki, K. Tamaoka, and Z. Wei, New holographic generalization of entanglement entropy, Phys. Rev. D 103 (2021), no. 2 026005 [arXiv:2005.13801] [INSPIRE].
A. Mollabashi, N. Shiba, T. Takayanagi, K. Tamaoka, and Z. Wei, Pseudo Entropy in Free Quantum Field Theories, Phys. Rev. Lett. 126 (2021), no. 8 081601 [arXiv:2011.09648] [INSPIRE].
A. Mollabashi, N. Shiba, T. Takayanagi, K. Tamaoka, and Z. Wei, Aspects of pseudoentropy in field theories, Phys. Rev. Res. 3 (2021), no. 3 033254 [arXiv:2106.03118] [INSPIRE].
Y. Aharonov, D.Z. Albert and L. Vaidman, How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100, Phys. Rev. Lett. 60 (1988) 1351 [INSPIRE].
J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, Colloquium: Understanding quantum weak values: Basics and applications, Rev. Mod. Phys. 86 (2014) 307.
W. Donnelly and A.C. Wall, Entanglement entropy of electromagnetic edge modes, Phys. Rev. Lett. 114 (2015), no. 11 111603 [arXiv:1412.1895] [INSPIRE].
H. Casini and M. Huerta, Entanglement entropy of a Maxwell field on the sphere, Phys. Rev. D 93 (2016), no. 10 105031 [arXiv:1512.06182] [INSPIRE].
H. Casini, M. Huerta, J.M. Magán, and D. Pontello, Logarithmic coefficient of the entanglement entropy of a Maxwell field, Phys. Rev. D 101 (2020), no. 6 065020 [arXiv:1911.00529] [INSPIRE].
S. Ghosh, R.M. Soni, and S.P. Trivedi, On The Entanglement Entropy For Gauge Theories, JHEP 09 (2015) 069 [arXiv:1501.02593] [INSPIRE].
R.M. Soni and S.P. Trivedi, Entanglement entropy in (3 + 1)-d free U(1) gauge theory, JHEP 02 (2017) 101 [arXiv:1608.00353] [INSPIRE].
J.R. David and J. Mukherjee, Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms, JHEP 01 (2021) 202 [arXiv:2005.08402] [INSPIRE].
V. Benedetti and H. Casini, Entanglement entropy of linearized gravitons in a sphere, Phys. Rev. D 101 (2020), no. 4 045004 [arXiv:1908.01800] [INSPIRE].
J.R. David and J. Mukherjee, Entanglement entropy of gravitational edge modes, JHEP 08 (2022) 065 [arXiv:2201.06043] [INSPIRE].
M. Nozaki, Notes on Quantum Entanglement of Local Operators, JHEP 10 (2014) 147 [arXiv:1405.5875] [INSPIRE].
M. Nozaki, T. Numasawa, and T. Takayanagi, Quantum Entanglement of Local Operators in Conformal Field Theories, Phys. Rev. Lett. 112 (2014) 111602 [arXiv:1401.0539] [INSPIRE].
M. Nozaki, T. Numasawa, and S. Matsuura, Quantum Entanglement of Fermionic Local Operators, JHEP 02 (2016) 150 [arXiv:1507.04352] [INSPIRE].
M. Nozaki and N. Watamura, Quantum Entanglement of Locally Excited States in Maxwell Theory, JHEP 12 (2016) 069 [arXiv:1606.07076] [INSPIRE].
P. Candelas and D. Deutsch, On the vacuum stress induced by uniform acceleration or supporting the ether, Proc. Roy. Soc. Lond. A 354 (1977) 79 [INSPIRE].
J.R. David and J. Mukherjee, Entanglement entropy of local gravitational quenches, arXiv:2209.05792 [INSPIRE].
J. Mukherjee, Partition functions of higher derivative conformal fields on conformally related spaces, JHEP 10 (2021) 236 [arXiv:2108.00929] [INSPIRE].
J. Mukherjee, Partition functions and entanglement entropy: Weyl graviton and conformal higher spin fields, JHEP 04 (2022) 071 [arXiv:2112.15461] [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: 2205.08179
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
Mukherjee, J. Pseudo Entropy in U(1) gauge theory. J. High Energ. Phys. 2022, 16 (2022). https://doi.org/10.1007/JHEP10(2022)016
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2022)016