Four-Impurity Operators and String Field Theory Vertex in the BMN Correspondence

TL;DR

This paper establishes a detailed correspondence between four-impurity operators in Yang-Mills theory and four-oscillator string states within the BMN limit of AdS/CFT, confirming the agreement of gauge and string theory calculations.

Contribution

It explicitly demonstrates the matching of four-impurity operators with string states and compares matrix elements from gauge theory and string field theory, extending previous two- and three-impurity results.

Findings

Gauge-theory matrix elements agree with string theory calculations.

Results extend the correspondence to four-impurity operators.

Agreement with perturbative gauge-theory methods is confirmed.

Abstract

In the context of the Penrose/BMN limit of the AdS/CFT correspondence, we consider four-impurity BMN operators in Yang-Mills theory, and demonstrate explicitly their correspondence to four-oscillator states in string theory. Using the dilatation operator on the gauge-theory side of the correspondence, we calculate matrix elements between four-impurity states. Since conformal dimensions of gauge-theory operators correspond to light-cone energies of string states, these matrix elements may be compared with the string-theory light-cone Hamiltonian matrix elements calculated in the plane-wave background using the string field theory vertex. We find that the two calculations agree, extending the cases of two- and three-impurity operators considered in the literature using BMN gauge-theory quantum mechanics. The results are also in agreement with calculations in the literature based on perturbative gauge-theory methods.