<p>We study the index of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathcal {N}=4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">N</mi> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> Yang–Mills theory on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$S^3\times \mathbb {R}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>S</mi> <mn>3</mn> </msup> <mo>×</mo> <mi mathvariant="double-struck">R</mi> </mrow> </math></EquationSource> </InlineEquation> at large angular momenta. A generalized Cardy limit exhibits macroscopic entropy at large <i>N</i>. Our result is derived using free QFT analysis, and also a background field method on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$S^3$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>S</mi> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>. The index sets a lower bound on the entropy. It saturates the Bekenstein–Hawking entropy of known supersymmetric AdS<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$_5$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>5</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> black holes, thus accounting for their microstates. We further analyze the so-called MacDonald index, exploring small black holes and possibly new black holes reminiscent of hairy black holes. Finally, we study aspects of large supersymmetric AdS<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$_7$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>7</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> black holes, using background field method on <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$S^5$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>S</mi> <mn>5</mn> </msup> </math></EquationSource> </InlineEquation> and ’t Hooft anomalies.</p>

Large AdS black holes from QFT

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2026年6月19日

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Sunjin Choi,
Joonho Kim,
Seok Kim,
June Nahmgoong

摘要

We study the index of $\mathcal {N}=4$ $N = 4$ Yang–Mills theory on $S^3\times \mathbb {R}$ $S^{3} \times R$ at large angular momenta. A generalized Cardy limit exhibits macroscopic entropy at large N. Our result is derived using free QFT analysis, and also a background field method on $S^3$ $S^{3}$ . The index sets a lower bound on the entropy. It saturates the Bekenstein–Hawking entropy of known supersymmetric AdS $_5$ $_{5}$ black holes, thus accounting for their microstates. We further analyze the so-called MacDonald index, exploring small black holes and possibly new black holes reminiscent of hairy black holes. Finally, we study aspects of large supersymmetric AdS $_7$ $_{7}$ black holes, using background field method on $S^5$ $S^{5}$ and ’t Hooft anomalies.