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

Abstract: We propose that generalized symmetries in some string-constructed QFTs are given by twisted K-theory, so as to be manifestly compatible with T-duality. We thus have even-form and odd-form symmetries determined by $K^*_N(\partial X)$, the twisted K-theory as D-brane charges on the asymptotic boundary $\partial X$ of internal geometry $X$ with twist class $N$. For these QFTs, "$p$-form symmetries" are no longer separately well-defined for individual $p$, but instead mixed up. We discuss 6D ADE-type (2,0) SCFTs and some 6d (1,0) LSTs as examples and demonstrate their twisted K-theoretic symmetries to be compatible with T-duality.