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<p>We re-examine the computation of the one-loop partition function of Type II supergravity theory compactified on <i>AdS</i><sub>3</sub> × <b>S</b><sup>3</sup> × <i>X</i>, where <i>X</i> can be <i>K</i><sub>3</sub>, <i>T</i> <sup>4</sup> and <b>S</b><sup>3</sup> × <b>S</b><sup>1</sup>. These backgrounds preserve eight supercharges (four left and four right moving) and are known to be holographically dual to either small or large <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = (4, 4) superconformal field theories. By extending well-established heat kernel techniques, we evaluate the one-loop determinants associated to these supergravity backgrounds. The resulting expressions are then used to reconstruct the characters of short multiplets of the corresponding dual boundary theories. A distinctive aspect of our analysis is the emergence of contributions from multiple gravitational saddle points in the path integral, reflecting the spectral flow structure present in the boundary theory.</p>

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One-loop determinants in AdS3 supergravity with extended supersymmetry

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月28日

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  • Ilija Rakic,
  • Lorenzo Toni

摘要

We re-examine the computation of the one-loop partition function of Type II supergravity theory compactified on AdS3 × S3 × X, where X can be K3, T 4 and S3 × S1. These backgrounds preserve eight supercharges (four left and four right moving) and are known to be holographically dual to either small or large N \( \mathcal{N} \) = (4, 4) superconformal field theories. By extending well-established heat kernel techniques, we evaluate the one-loop determinants associated to these supergravity backgrounds. The resulting expressions are then used to reconstruct the characters of short multiplets of the corresponding dual boundary theories. A distinctive aspect of our analysis is the emergence of contributions from multiple gravitational saddle points in the path integral, reflecting the spectral flow structure present in the boundary theory.