Holographic cubic vertex in the pp-wave

TL;DR

This paper revisits and extends the cubic interaction vertex in IIB string theory on the pp-wave background, providing a new vertex consistent with supergravity limits, holographic duality, and symmetry considerations.

Contribution

It introduces a new cubic vertex for IIB string theory in the pp-wave background that unifies previous proposals and aligns with supergravity and holographic duality.

Findings

Complete determination of the supergravity vertex.

Extension to a full string theory vertex with additional terms.

Consistency with the holographic duality map and symmetry realization.

Abstract

We revisit the cubic interaction of IIB string theory in the maximally supersymmetric pp-wave background. In the supergravity limit, we show that detailed comparison with AdS supergravity determine the vertex completely. Extension of this supergravity vertex to the full string theory leads to a new cubic vertex that combines the previous proposals and contains additional terms. We give an alternative derivation of the holographic duality map in supergravity, first found by Dobashi and Yoneya (hep-th/0406225) and show that our new vertex is consistent with it. We compare some non-BPS amplitudes (including impurity non-preserving ones) with the corresponding field theory correlators, and discuss what they imply for the stringy generalization of the duality map. We also notice that our vertex realizes the U(1)_Y symmetry linearly, and propose a similar modification for the flat space vertex.