New tests of the pp-wave correspondence

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-wavebackground and the dilatation operator Delta in N=4 Super Yang-Mills in thedouble scaling limit. We calculate matrix elements of these operators in stringfield theory and in gauge theory.In the string theory Hilbert space we use thenatural string basis,and in the gauge theory we use the basis which isisomorphic to it. States in this basis are specific linear combinations of theoriginal BMN operators, and were constructed previously for the case of twoscalar impurities. We extend this construction to incorporate BMN operatorswith vector and mixed impurities. This enables us to verify from the gaugetheory perspective two key properties of the three-string interaction vertex ofSpradlin and Volovich: (1) the vanishing of the three-string amplitude forstring states with one vector and one scalar impurity; and (2) the relativeminus sign in the string amplitude involving states with two vector impuritiescompared to that with two scalar impurities. This implies a spontaneousbreaking of the Z_2 symmetry of the string field theory in the pp-wavebackground. Furthermore, we calculate the gauge theory matrix elements of Delta-J for states with an arbitrary number of scalar impurities. In all cases wefind perfect agreement with the corresponding string amplitudes derived fromthe three-string vertex.Comment: 40 pages, 9 figure