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<p>We analyze causality and unitarity constraints in graviton scattering amplitudes, aiming to establish new bounds on theories with U(1)-gravitational anomalies, such as axion models or strongly-coupled gauge theories. For this purpose, we show the necessity of coupling these theories to gravity. We obtain a universal scale Λ<sub>caus</sub> at which states with <i>J</i> ≥ 4 must appear in the theory. We show that this scale can lie below the quantum gravity scale. For axion models, we get Λ<sub>caus</sub> ∼ <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26189_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sqrt{{M}_{P}{f}_{a}}\)</EquationSource> </InlineEquation> where <i>f</i><sub><i>a</i></sub> is the axion decay constant. In strongly-coupled gauge theories in the large-<i>N</i><sub><i>c</i></sub> limit, the presence of glueballs allows to evade these bounds, provided the number of fermions <i>N</i><sub><i>F</i></sub> ≪ <i>N</i><sub><i>c</i></sub> and the ’tHooft coupling is not large. Nevertheless, for models that have a holographic 5D dual (large ’tHooft coupling), Λ<sub>caus</sub> emerges as a new cutoff scale, unless certain conditions on the parameters of the 5D models are satisfied.</p>

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Bootstrapping the chiral-gravitational anomaly

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月14日

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  • Zi-Yu Dong,
  • Teng Ma,
  • Alex Pomarol,
  • Francesco Sciotti

摘要

We analyze causality and unitarity constraints in graviton scattering amplitudes, aiming to establish new bounds on theories with U(1)-gravitational anomalies, such as axion models or strongly-coupled gauge theories. For this purpose, we show the necessity of coupling these theories to gravity. We obtain a universal scale Λcaus at which states with J ≥ 4 must appear in the theory. We show that this scale can lie below the quantum gravity scale. For axion models, we get Λcaus ∼ \(\sqrt{{M}_{P}{f}_{a}}\) where fa is the axion decay constant. In strongly-coupled gauge theories in the large-Nc limit, the presence of glueballs allows to evade these bounds, provided the number of fermions NF ≪ Nc and the ’tHooft coupling is not large. Nevertheless, for models that have a holographic 5D dual (large ’tHooft coupling), Λcaus emerges as a new cutoff scale, unless certain conditions on the parameters of the 5D models are satisfied.