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<p>The spectrum and dynamics of near-extremal black holes is strongly modified by quantum effects at low temperatures. When the extremal limit does not preserve any supersymmetry, the density of states goes to zero at extremality and no extremal black holes remain. However, when the extremal limit is supersymmetric, a large microscopic degeneracy survives and there is a gap to the first excited black hole visible from gravity. In this article we study large <i>N</i> quantum mechanical models where supersymmetry is explicitly broken, allowing us to interpolate between these two qualitatively different pictures. We propose and analyze deformations of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26474_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 SYK models with such a pattern of (super) symmetry breaking which violate the U(1) <i>R</i>-symmetry. These models feature a lifting of the BPS degeneracy and a closing of the spectral gap, and we further show that the large <i>N</i> soft effective action is given by a modification of the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26474_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 Schwarzian theory in which the U(1)<sub><i>R</i></sub> mode becomes massive.</p>

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Supersymmetry breaking in SYK and the black hole spectrum

  • 期刊论文

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  • 发表日期：

    2025年6月17日

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  • Matthew Heydeman,
  • Yifei Liu,
  • Gustavo J. Turiaci

摘要

The spectrum and dynamics of near-extremal black holes is strongly modified by quantum effects at low temperatures. When the extremal limit does not preserve any supersymmetry, the density of states goes to zero at extremality and no extremal black holes remain. However, when the extremal limit is supersymmetric, a large microscopic degeneracy survives and there is a gap to the first excited black hole visible from gravity. In this article we study large N quantum mechanical models where supersymmetry is explicitly broken, allowing us to interpolate between these two qualitatively different pictures. We propose and analyze deformations of N \( \mathcal{N} \) = 2 SYK models with such a pattern of (super) symmetry breaking which violate the U(1) R-symmetry. These models feature a lifting of the BPS degeneracy and a closing of the spectral gap, and we further show that the large N soft effective action is given by a modification of the N \( \mathcal{N} \) = 2 Schwarzian theory in which the U(1)R mode becomes massive.