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<p>This paper focuses on a conformal block with rank <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27218_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </math></EquationSource> <EquationSource Format="TEX">\( \frac{3}{2} \)</EquationSource> </InlineEquation> irregular singularity which corresponds to the prepotential of the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27218_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">H</mi> <mn>1</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {\mathcal{H}}_1 \)</EquationSource> </InlineEquation> Argyres-Douglas theory in Ω background. We derive this irregular conformal block using the generalized holomorphic anomaly recursion relation. This results in an expression which is a power series in Ω-background parameters <i>ϵ</i><sub>1<i>,</i>2</sub> and exact in coupling. We have verified that in the small coupling regime our result is consistent with previously known expressions.</p><p>Furthermore we derive the Deformed Seiberg-Witten curve which provides an alternative tool to explore the above mentioned theory in Nekrasov-Shatashvili limit of Ω-background. We checked that the results are in complete agreement with the holomorphic anomaly approach.</p>

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A note on rank \( \frac{3}{2} \) Liouville irregular block

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  • 发表日期：

    2025年9月17日

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  • Rubik Poghossian,
  • Hasmik Poghosyan

摘要

This paper focuses on a conformal block with rank 3 2 \( \frac{3}{2} \) irregular singularity which corresponds to the prepotential of the H 1 \( {\mathcal{H}}_1 \) Argyres-Douglas theory in Ω background. We derive this irregular conformal block using the generalized holomorphic anomaly recursion relation. This results in an expression which is a power series in Ω-background parameters ϵ1,2 and exact in coupling. We have verified that in the small coupling regime our result is consistent with previously known expressions.

Furthermore we derive the Deformed Seiberg-Witten curve which provides an alternative tool to explore the above mentioned theory in Nekrasov-Shatashvili limit of Ω-background. We checked that the results are in complete agreement with the holomorphic anomaly approach.