Averaged null energy condition from causality

By Thomas Hartman, Sandipan Kundu, Amirhossein Tajdini. Journal of High Energy Physics, 2016

233 citations recorded by the source corpus.

Unitary, Lorentz-invariant quantum field theories in flat spacetime obey mi-crocausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, we show that this implies that the averaged null energy, ∫ duTuu, must be non-negative. This non-local operator appears in the operator product expansion of local operators in the lightcone limit, and therefore contributes to n-point functions. We derive a sum rule that isolates this contribution and is manifestly positive. The argument also applies to certain higher spin operators other than the stress tensor, generating an infinite family of new constraints of the form ∫ duXuuu···u ≥ 0. These lead to new inequalities for the coupling constants of spinning operators in conformal field theory, which include as special cases (but are generally stronger than) the existing constraints from the lightcone bootstrap, deep inelastic scattering, conformal collider methods, and relative entropy. We also comment on the relation to the recent derivation of the averaged null energy condition from relative entropy, and suggest a more general connection between causality and information-theoretic inequalities in QFT.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b095fe715e4ad779ade5fbeeeba9c1ef1ff1951c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

A general proof of the quantum null energy condition (2017, background): “˝ J ˇ Z R d˙˙J 2 [1 ReF] 0(7.47) { 64 { This is now a higher spin version of the QNEC. If we integrate this up, by taking x to innity, we recover the higher spin version of the ANEC rst studied in [19]. The QNEC is a more local version and indeed gives a local bound on the expectation value of a hig”
Regular Black Holes with Asymptotically Minkowski Cores (2019, background): “Let us now analyse the various energy conditions [49–60] and see whether they are violated in our spacetime.”
Loops in AdS from conformal field theory (2016, background): “Knowing loop amplitudes in a given bulk theory would open the door to nonplanar extensions of dynamical aspects of holography and the conformal bootstrap [34–50].”
The conformal bootstrap: Theory, numerical techniques, and applications (2018, methodology): “Two general proofs of the ANEC were given recently, one via quantum information (Faulkner et al., 2016), and one by causality (Hartman et al., 2017).44 Specializing to CFTs, the causality argument makes it clear that the ANEC is not an extra assumption but follows from other CFT axioms such as…”
De Sitter Space and the Swampland (2018, background): “It would be interesting to find out if a bound on |∇V |/V can be obtained with the averaged null energy condition, which is weaker and is known to be satisfied by any unitary quantum field theory [41, 42].”
Light-ray operators in conformal field theory (2018, methodology): “is point. – 64 – 6 Positivityand the ANEC The average null energy condition (ANEC) states that E = L[T] is a positive-semideﬁnite operator. The ANEC was proven in [45] using information theory and in [46] using causality. The causality-based proof [46] proceeds by isolating the contribution of E in ”
Modular Hamiltonians on the null plane and the Markov property of the vacuum state (2017, background): “Using results on algebraic QFT and the averaged null energy condition (ANEC) proved in [12, 13], we show that the operators (1.7) are in fact the full modular Hamiltonians for the regions R γ .”
Analyticity in spin in conformal theories (2017, background): “Convergence will be established for all spins higher than one, by borrowing ideas from the recent “bound on chaos” as well as from a recent proof of the averaged null energy condition (ANEC) [20, 21], which are reviewed in the next section.”
Weight shifting operators and conformal blocks (2017, unknown): “Subsequently, techniques for computing blocks of operators with spin [35, 69–77] have led to universal numerical bounds on wide classes of CFTs [35, 66, 78], in addition to analytical results like proofs of the conformal collider bounds [79–82] and the average null energy condition [83], and new res”