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<p>For a variety of BPS black holes in string theory, the supersymmetric index has provided a microscopic validation of the Bekenstein-Hawking formula. In the near-BPS limit, a gravitational path integral analysis previously revealed the semiclassical spectrum is modified, having a large extremal degeneracy (consistent with the index) and a mass gap up to a continuum of non-BPS black holes. Presently, we study examples in which these sharp features of the spectrum are altered due to the presence of anomalies in the form of <i>ϑ</i>-angle terms in the action. These may appear generally, but we focus on near-BPS dyonic AdS<sub>4</sub> black holes in M-theory, dual to 3d <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26507_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 2 SCFTs of Class <i>R</i> obtained by twisted compactification of <i>N</i> wrapped M5 branes. Due to the Witten effect, the dyonic black holes receive quantum corrections to their charges, and when <i>ϑ</i> = <i>π</i> one may find a mixed ‘t Hooft anomaly between the U(1)<sub><i>R</i></sub> and <i>ℤ</i><sub>2</sub> time reversal symmetries. Using results from <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26507_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 2 JT supergravity, we find these effects result in a spectrum in which both the gap and index are reduced, and may even vanish. Surprisingly, for <i>ϑ</i> → <i>π</i>, neither the Bekenstein-Hawking formula nor the index correctly account for the extremal degeneracies.</p>

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Mixed ’t Hooft anomalies and the Witten effect for AdS black holes

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  • 发表日期：

    2025年6月19日

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  • Matthew Heydeman,
  • Chiara Toldo

摘要

For a variety of BPS black holes in string theory, the supersymmetric index has provided a microscopic validation of the Bekenstein-Hawking formula. In the near-BPS limit, a gravitational path integral analysis previously revealed the semiclassical spectrum is modified, having a large extremal degeneracy (consistent with the index) and a mass gap up to a continuum of non-BPS black holes. Presently, we study examples in which these sharp features of the spectrum are altered due to the presence of anomalies in the form of ϑ-angle terms in the action. These may appear generally, but we focus on near-BPS dyonic AdS4 black holes in M-theory, dual to 3d N \( \mathcal{N} \) = 2 SCFTs of Class R obtained by twisted compactification of N wrapped M5 branes. Due to the Witten effect, the dyonic black holes receive quantum corrections to their charges, and when ϑ = π one may find a mixed ‘t Hooft anomaly between the U(1)R and ℤ2 time reversal symmetries. Using results from N \( \mathcal{N} \) = 2 JT supergravity, we find these effects result in a spectrum in which both the gap and index are reduced, and may even vanish. Surprisingly, for ϑ → π, neither the Bekenstein-Hawking formula nor the index correctly account for the extremal degeneracies.