Abstract
We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT_22). We show that QNEC saturates for all states dual to vacuum solutions of AdS_33 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_22 with a global quench dual to AdS_33-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_33 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/4h/4 in the large h expansion.
Highlights
In most of the paper we stay in the usual AdS3/CFT2 context, i.e., on the bulk side we study Einstein gravity with standard asymptotic AdS3 boundary conditions [16], whose solutions in absence of matter are given by the Bañados geometries [17]
For illustration we focus here on the Bañados geometry associated with a hot-cold heat bath coupling with a steady state heat current, which serves as a holographic model for far from equilibrium flow in quantum critical systems [18, 19]
In this subsection we summarize our numerical results for holographic entanglement entropy (HEE) and Quantum Null Energy Condition (QNEC) in 1+1 dimensional globally quenched systems with holographic duals given by AdS3-Vaidya spacetimes
Summary
The Quantum Null Energy Condition (QNEC) [1] is a local energy condition that has attracted a lot of interest in recent years [2,3,4,5,6,7,8,9,10], since it can be shown to hold universally for quantum field theories in more than two dimensions (given some assumptions like unitarity) [11]. We consider as example far from equilibrium flow in quantum critical systems [18,19] and show that QNEC saturates. Adding bulk matter makes QNEC2 even more interesting, as it no longer needs to saturate. We consider AdS3-Vaidya geometries, which provide a gravity dual to the thermalization of a global quench on the CFT2 side [20,21,22,23,24] and find a curious novel feature of QNEC half-saturation.
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