Impurity Non-Preserving 3-Point Correlators of BMN Operators from PP-Wave Holography II : Fermionic Excitations

TL;DR

This paper confirms the holographic duality between string interactions and gauge theory OPE coefficients for fermionic BMN operators, emphasizing the importance of operator mixing in the pp-wave limit.

Contribution

It extends previous holographic duality results to impurity non-preserving processes involving fermionic excitations, highlighting the role of operator mixing.

Findings

Duality relation holds at leading order in large μ limit.

Operator mixing is essential for matching string states with gauge operators.

Results support the general validity of the duality for various impurity processes.

Abstract

The holographic principle in the pp-wave limit proposed in our previous works is further confirmed by studying impurity non-preserving processes which contain a fermionic BMN operator with one scalar and one fermion impurities. We show that the previously proposed duality relation between the matrix elements of the three point interaction Hamiltonian in the holographic string field theory and the OPE coefficients in super Yang-Mills theory holds to the leading order in the large $\mu$ limit. Operator mixing is required to obtain the BMN operator of definite conformal dimension which corresponds to the string state with one scalar and one fermion excitations. The mixing term plays a crucial role for our duality relation to be valid. Our results, combined with those in the previous papers, provide a positive support that our duality relation holds for the general process regardless of the kind of impurities and of whether impurities conserve or not.