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<p>The restricted quantum focusing conjecture (rQFC) plays a central role in an axiomatic formulation of semiclassical gravity. Since much hinges on its validity, it is imperative to subject the rQFC to rigorous tests in novel settings. Here we do so in two independent directions.</p><p>First, we prove rQFC in a class of spacetime dimension <i>d</i> = 2 toy models, JT gravity coupled to a QFT. We also construct explicit counter-examples to the original and <i>stronger</i> Quantum Focusing Conjecture in a regime where matter quantum effects are comparable to the total dilaton value.</p><p>Second, for <i>d &gt;</i> 2, we derive from the rQFC a constraint stronger than the Quantum Null Energy Condition (QNEC). In a broad class of states, this bound forbids the QNEC from saturating faster than <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi>O</mi> <mfenced close=")" open="("> <mi mathvariant="script">A</mi> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( O\left(\mathcal{A}\right) \)</EquationSource> </InlineEquation> as the transverse area <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">A</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{A} \)</EquationSource> </InlineEquation> of a certain null deformation shrinks to zero. We speculate about a universal strengthened QNEC holding across all QFT states.</p>

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Tests of restricted quantum focusing and a new CFT bound

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月11日

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  • Victor Franken,
  • Sami Kaya,
  • François Rondeau,
  • Arvin Shahbazi-Moghaddam,
  • Patrick Tran

摘要

The restricted quantum focusing conjecture (rQFC) plays a central role in an axiomatic formulation of semiclassical gravity. Since much hinges on its validity, it is imperative to subject the rQFC to rigorous tests in novel settings. Here we do so in two independent directions.

First, we prove rQFC in a class of spacetime dimension d = 2 toy models, JT gravity coupled to a QFT. We also construct explicit counter-examples to the original and stronger Quantum Focusing Conjecture in a regime where matter quantum effects are comparable to the total dilaton value.

Second, for d > 2, we derive from the rQFC a constraint stronger than the Quantum Null Energy Condition (QNEC). In a broad class of states, this bound forbids the QNEC from saturating faster than O A \( O\left(\mathcal{A}\right) \) as the transverse area A \( \mathcal{A} \) of a certain null deformation shrinks to zero. We speculate about a universal strengthened QNEC holding across all QFT states.