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<p>We study the global forms of class <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">S</mi> <mfenced close="]" open="["> <msub> <mi>A</mi> <mrow> <mi>N</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{S}\left[{A}_{N-1}\right] \)</EquationSource> </InlineEquation> 4d <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 2 theories by deriving their defect groups (charges of line operators up to screening by local operators) from Coulomb branch data. Specifically, we employ an explicit construction of the BPS quiver for the case of full regular punctures to show that the defect group is (<i>ℤ</i><sub><i>N</i></sub>)<sup>2<i>g</i></sup>, where <i>g</i> is the genus of the associated Riemann surface. This determines a sector of surface operators in the 5d symmetry TFT. We show how these can also be identified from dimensional reduction of M-theory. We discuss connections to the theory of cluster algebras.</p>

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Defect groups of class \( \mathcal{S} \) theories from the Coulomb branch

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  • 发表日期：

    2025年1月28日

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  • Elias Riedel Gårding

摘要

We study the global forms of class S A N − 1 \( \mathcal{S}\left[{A}_{N-1}\right] \) 4d N \( \mathcal{N} \) = 2 theories by deriving their defect groups (charges of line operators up to screening by local operators) from Coulomb branch data. Specifically, we employ an explicit construction of the BPS quiver for the case of full regular punctures to show that the defect group is (ℤN)2g, where g is the genus of the associated Riemann surface. This determines a sector of surface operators in the 5d symmetry TFT. We show how these can also be identified from dimensional reduction of M-theory. We discuss connections to the theory of cluster algebras.