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

TL;DR

This paper applies K-theory to classify topological patterns of fermionic operator mixing in holographic conformal field theories via the AdS/CFT correspondence.

Contribution

It introduces a K-theoretic framework to classify fermionic operator mixing patterns in holographic CFTs, linking topological insulator classifications to AdS/CFT.

Findings

Classified topological classes of fermionic operators in holographic CFTs.

Established a correspondence between fermionic mass matrices and operator mixing patterns.

Extended topological classification methods to holographic duals.

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.