WWDC26：2026 年 6 月 8 日至 12 日 (太平洋时间)

Spin-1/2 kagome-lattice Heisenberg antiferromagnet is theoretically known to have a quantum spin liquid ground state, one of the frontiers of condensed matter physics. The search for the model substances has been continued for a long time, and many candidate substances have been reported. Most of them are hydroxide minerals. Here, I review the static and dynamic properties of non-mineral kagome-lattice antiferromagnets Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$.

We show that three-dimensional N=8 $Sp(N)$ and $SO(2N+1)$ gauge theories flow to the same strong coupling fixed point. As a consequence, the corresponding orientifold two-planes in type IIA string theory are described at strong coupling and low-energies by the same M theory background. In the large $N$ limit, these assertions are confirmed by studying discrete torsion in the supergravity theory corresponding to membranes on $R^8/Z_2$.