TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.5.125
TI  - Multi-entropy at low Renyi index in 2d CFTs
PY  - 2024/05/13
UR  - https://scipost.org/SciPostPhys.16.5.125
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 5
SP  - 125
A1  - Harper, Jonathan
AU  - Takayanagi, Tadashi
AU  - Tsuda, Takashi
AB  - For a static time slice of AdS$_3$ we describe a particular class of minimal surfaces which form trivalent networks of geodesics. Through geometric arguments we provide evidence that these surfaces describe a measure of multipartite entanglement. By relating these surfaces to Ryu-Takayanagi surfaces it can be shown that this multipartite contribution is related to the angles of intersection of the bulk geodesics. A proposed boundary dual [Phys. Rev. D 106, 126001 (2022), J. High Energy Phys. 08, 202 (2023), J. High Energy Phys. 05, 008 (2023)], the multi-entropy, generalizes replica trick calculations involving twist operators by considering monodromies with finite group symmetry beyond the cyclic group used for the computation of entanglement entropy. We make progress by providing explicit calculations of Renyi multi-entropy in two dimensional CFTs and geometric descriptions of the replica surfaces for several cases with low genus. We also explore aspects of the free fermion and free scalar CFTs. For the free fermion CFT we examine subtleties in the definition of the twist operators used for the calculation of Renyi multi-entropy. In particular the standard bosonization procedure used for the calculation of the usual entanglement entropy fails and a different treatment is required.
ER  -

@Article{10.21468/SciPostPhys.16.5.125,
	title={{Multi-entropy at low Renyi index in 2d CFTs}},
	author={Jonathan Harper and Tadashi Takayanagi and Takashi Tsuda},
	journal={SciPost Phys.},
	volume={16},
	pages={125},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.5.125},
	url={https://scipost.org/10.21468/SciPostPhys.16.5.125},
}