By Shih-Ho Ho(CTP, MIT) and Feng-Li Lin(Dept. of Phys. of MIT and NTNU)

In this work, we classify the free massive Dirac fermion theories in the asymptotically AdS spaces (including AdS solitons) based on Kitaev’s framework of the K-theory analysis for classifying the topological insulators/superconductors. By the AdS/CFT correspondence, it is equivalent to classify the topological fermionic phases of the holographic dual theories, which are either strongly coupled gapless or gapped systems. Especially, our framework provides a way of classifying the topological phases for the strongly interacting gapless systems, of which the classification is intractable in the context of strongly correlated condensed matters mainly for gapped systems.