Generalized symmetries in string-constructed QFTs via K-theory

A bstract 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 K N ( ∂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 ℂ 3 and ℂ 4 . We also discuss the implications of these results in the dual brane descriptions.