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<p>We propose that generalized symmetries in some string-constructed QFTs are given by K-theory. We thus have <i>even-form</i> and <i>odd-form</i> symmetries determined by <i>K</i><sub><i>N</i></sub>(<i>∂X</i>), the twisted K-theory as D-brane charges on the asymptotic boundary <i>∂X</i> of internal geometry <i>X</i> with twist class <i>N</i>. For these QFTs, “<i>p-form symmetries</i>” are no longer separately well-defined for individual <i>p</i>, but are instead mixed together. We discuss 6D ADE-type (2,0) SCFTs and some 6d (1,0) LSTs as examples and demonstrate their twisted K-theoretic symmetries, and check that they are compatible with T-duality. We further point out, through explicit examples, that K-theory leads to symmetry extensions that cannot be detected by cohomology for Type II string theory on certain orbifolds of ℂ<sup>3</sup> and ℂ<sup>4</sup>. We also discuss the implications of these results in the dual brane descriptions.</p>

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Generalized symmetries in string-constructed QFTs via K-theory

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  • 发表日期：

    2026年5月12日

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  • Hao Y. Zhang

摘要

We propose that generalized symmetries in some string-constructed QFTs are given by K-theory. We thus have even-form and odd-form symmetries determined by KN(∂X), the twisted K-theory as D-brane charges on the asymptotic boundary ∂X of internal geometry X with twist class N. For these QFTs, “p-form symmetries” are no longer separately well-defined for individual p, but are instead mixed together. We discuss 6D ADE-type (2,0) SCFTs and some 6d (1,0) LSTs as examples and demonstrate their twisted K-theoretic symmetries, and check that they are compatible with T-duality. We further point out, through explicit examples, that K-theory leads to symmetry extensions that cannot be detected by cohomology for Type II string theory on certain orbifolds of ℂ3 and ℂ4. We also discuss the implications of these results in the dual brane descriptions.