# Quantum Null Energy Condition and its (non)saturation in 2d CFTs

### Submission summary

 As Contributors: Daniel Grumiller Arxiv Link: https://arxiv.org/abs/1901.04499v2 Date accepted: 2019-03-21 Date submitted: 2019-03-14 Submitted by: Grumiller, Daniel Submitted to: SciPost Physics Domain(s): Theoretical Subject area: High-Energy Physics - Theory

### 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.

### Ontology / Topics

See full Ontology or Topics database.

### List of changes

-) corrected the wording of the few remaining instances where 'QNEC' referred to the right hand side of the QNEC-inequality (addresses point 1 by referee)

-) minor text edits in section 3.2 in paragraphs after Eq. (3.5) (addresses point 2 by referee)

-) minor edits in section 6.3 after Eq. (6.7) and in footnote 11 for clarity, in particular introduction of bold faced letters for operators (addresses point 3 by referee)

### Submission & Refereeing History

Resubmission 1901.04499v2 on 14 March 2019
Submission 1901.04499v1 on 30 January 2019

## Reports on this Submission

### Report

The authors revised the manuscript and addressed the concerns raised in my report. I believe that the paper is now ready for publication.

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