Renormalized Entanglement Entropy and general entropic c−function

¹ School of Nuclear Science and Technology, University of South China, Hengyang 421001, China
² Center for Theoretical Physics and College of Physics, Jilin University, Changchun 130012, People’s Republic of China
³ Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Golm, Germany
⁴ School of Physics and Electronics, Central South University, Changsha 418003, China
⁵ Department of Physics and Astronomy, University of Alabama, 514 University Boulevard, Tuscaloosa, AL, 35487, USA

^* e-mail: fujitamitsutoshi@usc.edu.cn
^** e-mail: hesong@jlu.edu.cn
^*** e-mail: sunyuan@csu.edu.cn
^**** e-mail: jzhang163@crimson.ua.edu

Published online: 10 December 2024

Abstract

Holographic entanglement entropy (EE) and its renormalized form in AdS solitons with gauge potential are computed across a range of dimensions. The renormalized EE is identified as a cutoff-independent universal component of EE. By taking into account Kaluza-Klein reduction and the constraints of the low-energy limit, the (d − 1)-dimensional renormalized EE is deduced from the odd-dimensional counterpart. The region associated with the shrinking circle, which is examined at large values of l is indicative of this relationship. Transitions of the minimal surface are from a disk-shaped to a cylindrical configuration as l increases. A quantum phase transition occurs at a critical subregion size, with the renormalized EE exhibiting non-monotonic behavior in the vicinity of this size. In all dimensions, massive modes become decoupled at the low energy limit, whereas degrees of freedom that include Wilson lines influence the behavior at smaller energy scales.