PP-wave/Yang-Mills Correspondence: An Explicit Check

TL;DR

This paper provides explicit evidence for the correspondence between type IIB supergravity in a pp-wave background and dual supersymmetric Yang-Mills theory by constructing interaction Hamiltonians and comparing matrix elements.

Contribution

It constructs the cubic interaction Hamiltonian for supergravity and confirms the duality by matching matrix elements with Yang-Mills theory predictions.

Findings

Constructed the cubic interaction Hamiltonian for supergravity.

Fixed the normalization of light-cone string field theory.

Confirmed the duality by matching matrix elements with Yang-Mills theory.

Abstract

We present an explicit evidence that shows the correspondence between the type IIB supergravity in the pp-wave background and its dual supersymmetric Yang-Mills theory at the interaction level. We first construct the cubic term of the light-cone interaction Hamiltonian for the dilaton-axion sector of the supergravity. Our result agrees with the corresponding part of the light-cone string field theory (SFT) and furthermore fixes its previously undetermined $p^+$-dependent normalization. Adopting thus fixed light-cone SFT, we compute the matrix elements of light-cone Hamiltonian involving three chiral primary states and find an agreement with a prediction from the dual Yang-Mills theory.