Entropy variations and light ray operators from replica defects

Journal of High Energy Physics

Regular Article - Theoretical Physics

Arvin Shahbazi-Moghaddam¹  Adam Levine¹  Venkatesa Chandrasekaran¹  Thomas Faulkner²  Srivatsan Balakrishnan² 

[1] Center for Theoretical Physics and Department of Physics, University of California, 94720, Berkeley, CA, USA;Department of Physics, University of Illinois, 1110 W. Green St., 61801-3080, Urbana, IL, USA;

关键词: Boundary Quantum Field Theory;    Conformal Field Theory;    Field Theories in Higher Dimensions;   

DOI  :  10.1007/JHEP09(2022)217

 received in 2021-09-25, accepted in 2022-09-08,  发布年份 2022

来源: Springer

【 摘 要 】

We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as n approaches 1 a contact term can emerge when the OPE contains defect operators of twist d − 2. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the n → 1 limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap. As a check, we show independently that in a large class of near vacuum states, the second variation of the entanglement entropy is given by a simple correlation function of averaged null energy operators as studied by Hofman and Maldacena. This suggests that sub-leading terms in the defect OPE are controlled by a defect version of the spin-3 non-local light ray operator and we speculate about the possible origin of such a defect operator. For free theories this contribution condenses to a contact term that leads to violations of QNEC saturation.

【 授权许可】

Unknown   
© The Author(s) 2022