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<p>In a previous paper, we proposed an entropy function for AdS<sub>4</sub> BPS black holes in M-theory with general magnetic charges, resolving a long-standing puzzle about baryonic charges in three-dimensional holography and offering a prediction for the large-<i>N</i> limit of several partition functions whose saddle points have yet to be found. The entropy function is constructed from the master volume of the internal manifold. In this paper, we prove that the entropy of a general class of black holes based on toric geometry can indeed be reformulated as an <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26959_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">I</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{I} \)</EquationSource> </InlineEquation>-extremization problem, and we provide a set of examples. As an aside, we also simplify existing proofs of the equivalence between <i>a</i>-, <i>c</i>-, and <i>F</i>-extremizations and their gravitational duals.</p>

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\( \mathcal{I} \)-extremization for AdS4 black holes: master volume, free energy, and baryonic charges

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  • 发表日期：

    2025年8月13日

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  • Seyed Morteza Hosseini,
  • Alberto Zaffaroni

摘要

In a previous paper, we proposed an entropy function for AdS4 BPS black holes in M-theory with general magnetic charges, resolving a long-standing puzzle about baryonic charges in three-dimensional holography and offering a prediction for the large-N limit of several partition functions whose saddle points have yet to be found. The entropy function is constructed from the master volume of the internal manifold. In this paper, we prove that the entropy of a general class of black holes based on toric geometry can indeed be reformulated as an I \( \mathcal{I} \) -extremization problem, and we provide a set of examples. As an aside, we also simplify existing proofs of the equivalence between a-, c-, and F-extremizations and their gravitational duals.