Fermion BMN operators, the dilatation operator of N=4 SYM, and pp-wave string interactions

TL;DR

This paper investigates the fermionic sector of the BMN correspondence by comparing matrix elements of the dilatation operator in N=4 SYM with string interaction amplitudes, finding perfect agreement up to specified orders.

Contribution

It provides the first detailed comparison of fermionic BMN operators' matrix elements in field theory and string theory, confirming the correspondence at the quantum level.

Findings

Field theory and string theory matrix elements match perfectly.

Results confirm the fermionic BMN correspondence at one-loop order.

The study extends the BMN correspondence to include fermionic impurities.

Abstract

The goal of this paper is to study the BMN correspondence in the fermionic sector. On the field theory side, we compute matrix elements of the dilatation operator in N=4 Super Yang-Mills for BMN operators containing two fermion impurities. Our calculations are performed up to and including O(lambda') in the 't Hooft coupling and O(g_2) in the Yang-Mills genus counting parameter. On the string theory side, we compute the corresponding matrix elements of the interacting string Hamiltonian in string field theory, using the three-string interaction vertex constructed by Spradlin and Volovich (and subsequently elaborated by Pankiewicz and Stefanski). In string theory we use the natural string basis, and in field theory the basis which is isomorphic to it. We find that the matrix elements computed in field theory and the corresponding string amplitudes derived from the three-string vertex are, in all cases, in perfect agreement.