<p>We provide the spindle interpretations of previously known solutions, <i>AdS</i><sub>3</sub> × Σ × <i>S</i><sup>1</sup> × <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27379_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi>K</mi> <msubsup> <mi>E</mi> <mn>2</mn> <mo>+</mo> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( K{E}_2^{+} \)</EquationSource> </InlineEquation> × <i>T</i> <sup>2</sup> of type IIB supergravity and <i>AdS</i><sub>2</sub> × Σ × <i>S</i><sup>1</sup> × <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27379_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi>K</mi> <msubsup> <mi>E</mi> <mn>4</mn> <mo>+</mo> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( K{E}_4^{+} \)</EquationSource> </InlineEquation> × <i>T</i> <sup>2</sup> of eleven-dimensional supergravity, where Σ is a spindle factor. For the <i>AdS</i><sub>3</sub> solutions, the internal space of Σ × <i>S</i><sup>1</sup> × <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27379_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi>K</mi> <msubsup> <mi>E</mi> <mn>2</mn> <mo>+</mo> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( K{E}_2^{+} \)</EquationSource> </InlineEquation> was previously known as the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27379_Article_IEq4.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi mathvariant="script">Y</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">\( {\mathcal{Y}}^{p,q} \)</EquationSource> </InlineEquation> manifold, which shares the identical topology of the <i>Y</i> <sup><i>p</i>,<i>q</i></sup> manifolds. Unlike the previously known spindle solutions, the gauged supergravity origin and the field theory dual of the solutions are not clear at the moment. We perform the flux quantizations and calculate the holographic central charge and the Bekenstein-Hawking entropy of the presumed black hole solutions, respectively.</p>

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AdS solutions with spindle factors

  • Minwoo Suh

摘要

We provide the spindle interpretations of previously known solutions, AdS3 × Σ × S1 × K E 2 + \( K{E}_2^{+} \) × T 2 of type IIB supergravity and AdS2 × Σ × S1 × K E 4 + \( K{E}_4^{+} \) × T 2 of eleven-dimensional supergravity, where Σ is a spindle factor. For the AdS3 solutions, the internal space of Σ × S1 × K E 2 + \( K{E}_2^{+} \) was previously known as the Y p , q \( {\mathcal{Y}}^{p,q} \) manifold, which shares the identical topology of the Y p,q manifolds. Unlike the previously known spindle solutions, the gauged supergravity origin and the field theory dual of the solutions are not clear at the moment. We perform the flux quantizations and calculate the holographic central charge and the Bekenstein-Hawking entropy of the presumed black hole solutions, respectively.