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<p>We show the existence of infinitely many Bethe expansions for general four dimensional superconformal theories. We then propose an analytic method to systematically obtain all the Bethe solutions, both isolated and continuous, for general superconformal theories. In particular, we show that the contribution from the continuous manifold of solutions to the index comes from isolated points on this manifold. We check our proposals on <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 4 SYM. For U(3) or SU(3), which are the first examples with continuous solutions, we demonstrate the non-trivial cancellation between the tachyon contributions from the previously known isolated solutions and those from the continuous solutions.</p>

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Generalized Bethe expansions of superconformal indices

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月18日

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  • Alejandro Cabo-Bizet,
  • Wei Li

摘要

We show the existence of infinitely many Bethe expansions for general four dimensional superconformal theories. We then propose an analytic method to systematically obtain all the Bethe solutions, both isolated and continuous, for general superconformal theories. In particular, we show that the contribution from the continuous manifold of solutions to the index comes from isolated points on this manifold. We check our proposals on N \( \mathcal{N} \) = 4 SYM. For U(3) or SU(3), which are the first examples with continuous solutions, we demonstrate the non-trivial cancellation between the tachyon contributions from the previously known isolated solutions and those from the continuous solutions.