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

TL;DR

This paper proposes that generalized symmetries in certain string-constructed quantum field theories are classified by K-theory, revealing complex symmetry structures compatible with T-duality and extending beyond cohomological classifications.

Contribution

It introduces K-theory as a framework for understanding generalized symmetries in string-derived QFTs, including mixed p-form symmetries and symmetry extensions not detectable by cohomology.

Findings

K-theoretic symmetries are demonstrated in 6D SCFTs and LSTs.

Symmetry structures are compatible with T-duality.

K-theory reveals symmetry extensions beyond cohomology in string orbifolds.

Abstract

We propose that generalized symmetries in some string-constructed QFTs are given by K-theory. We thus have \textit{even-form} and \textit{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, ``\textit{$p$-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 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.