K-theoretic classification of fermionic operator mixings in holographic conformal field theories

Abstract

In this paper, we apply the K-theory scheme of classifying the topological insulators/superconductors to classify the topological classes of the massive multi-flavor fermions in anti-de Sitter (AdS) space. In the context of AdS/CFT correspondence, the multi-flavor fermionic mass matrix is dual to the pattern of operator mixing in the boundary conformal field theory (CFT). Thus, our results classify the possible patterns of operator mixings among fermionic operators in the holographic CFT.

25 pages, 2 figures, 6 tables; v2 the results in section 4 are refined; v3 title changed; v4 title change and revised text for the final published version