New tests of the pp-wave correspondence

TL;DR

This paper verifies the pp-wave/SYM correspondence by calculating and comparing matrix elements of string and gauge theory operators, extending previous constructions to include vector and mixed impurities, and confirming key properties of the three-string interaction vertex.

Contribution

It extends the construction of BMN operators to include vector and mixed impurities and verifies key properties of the three-string interaction vertex from the gauge theory perspective.

Findings

Confirmed vanishing of three-string amplitude with one vector and one scalar impurity.

Observed a minus sign in amplitudes with two vector impurities, indicating Z_2 symmetry breaking.

Achieved perfect agreement between gauge theory matrix elements and string amplitudes for states with multiple impurities.

Abstract

The pp-wave/SYM correspondence is an equivalence relation, H_{string}= Delta -J, between the Hamiltonian H_{string} of string field theory in the pp-wave background and the dilatation operator Delta in N=4 Super Yang-Mills in the double scaling limit. We calculate matrix elements of these operators in string field theory and in gauge theory.In the string theory Hilbert space we use the natural string basis,and in the gauge theory we use the basis which is isomorphic to it. States in this basis are specific linear combinations of the original BMN operators, and were constructed previously for the case of two scalar impurities. We extend this construction to incorporate BMN operators with vector and mixed impurities. This enables us to verify from the gauge theory perspective two key properties of the three-string interaction vertex of Spradlin and Volovich: (1) the vanishing of the three-string amplitude for string states with one vector and one scalar impurity; and (2) the relative minus sign in the string amplitude involving states with two vector impurities compared to that with two scalar impurities. This implies a spontaneous breaking of the Z_2 symmetry of the string field theory in the pp-wave background. Furthermore, we calculate the gauge theory matrix elements of Delta -J for states with an arbitrary number of scalar impurities. In all cases we find perfect agreement with the corresponding string amplitudes derived from the three-string vertex.