K-theoretic Global Symmetry in String-constructed QFT and T-duality

We propose that generalized symmetries in some string-constructed QFTs are given by K-theory. We thus have $\mathit{\text{even-form}}$ and $\mathit{\text{odd-form}}$ symmetries determined by $K_N(\mathrm{\partial }X)$, the twisted K-theory as D-brane charges on the asymptotic boundary $\mathrm{\partial }X$ of internal geometry $X$ with twist class $N$. For these QFTs, ``$p\mathit{\text{-form}}\mathit{\text{symmetries}}$" 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 we checked them to be 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 ${\mathbb{C}}^3$ and ${\mathbb{C}}^4$. We also discuss the implications of these results in the dual brane descriptions.