## Quantum null energy condition and its (non)saturation in 2d CFTs

Christian Ecker, Daniel Grumiller, Wilke van der Schee, Shahin Sheikh-Jabbari, Philipp Stanzer

SciPost Phys. 6, 036 (2019) · published 25 March 2019

- doi: 10.21468/SciPostPhys.6.3.036
- Submissions/Reports

### Abstract

We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT$_2$). We show that QNEC saturates for all states dual to vacuum solutions of AdS$_3$ Einstein gravity, including systems that are far from thermal equilibrium. If the Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be saturated, whereby we give both analytical and numerical examples. In particular, for CFT$_2$ with a global quench dual to AdS$_3$-Vaidya geometries we find a curious half-saturation of QNEC for large entangling regions. We also address order one corrections from quantum backreactions of a scalar field in AdS$_3$ dual to a primary operator of dimension $h$ in a large central charge expansion and explicitly compute both, the backreacted Ryu--Takayanagi surface part and the bulk entanglement contribution to EE and QNEC. At leading order for small entangling regions the contribution from bulk EE exactly cancels the contribution from the back-reacted Ryu-Takayanagi surface, but at higher orders in the size of the region the contributions are almost equal while QNEC is not saturated. For a half-space entangling region we find that QNEC is gapped by $h/4$ in the large $h$ expansion.

### Cited by 3

### Ontology / Topics

See full Ontology or Topics database.### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1 }^{2 }Christian Ecker, -
^{2 }Daniel Grumiller, -
^{1 }^{3 }Wilke van der Schee, -
^{4 }Shahin Sheikh-Jabbari, -
^{2 }Philipp Stanzer

^{1}Universiteit Utrecht / University of Utrecht [UU]^{2}Technische Universität Wien / Vienna University of Technology [TUW]^{3}Massachusetts Institute of Technology [MIT]^{4}پژوهشگاه دانشهای بنیادی / Institute for Research in Fundamental Sciences [IPM]

- Centro Internazionale di Fisica Teorica Abdus Salam / Abdus Salam International Centre for Theoretical Physics [ICTP]
- Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
- ISEF Foundation
- Iran National Science Foundation [INSF]
- Ministerie van Onderwijs, Cultuur en Wetenschap / Ministry of Education Culture and Science [OCW]
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek / Netherlands Organisation for Scientific Research [NWO]