Supersymmetric D3 brane and N=4 SYM actions in plane wave backgrounds

TL;DR

This paper derives the explicit form of the D3 brane action in a maximally supersymmetric plane wave background and explores its relation to N=4 SYM theory in similar backgrounds, with implications for AdS/CFT correspondence.

Contribution

It provides the all-order fermionic D3 brane action in a plane wave background and develops the Hamiltonian light cone gauge formulation of N=4 SYM in this setting.

Findings

D3 brane action simplifies in light cone gauge

N=4 SYM in plane wave background exhibits compatible symmetries

Potential applications in AdS/CFT duality

Abstract

The explicit (all-order in fermions) form of the kappa-symmetric $D3$ brane probe action was previously found in the two maximally supersymmetric type IIB vacua: flat space and $AdS_5 \times S^5$. Here we present the form of the action in the third maximally supersymmetric type IIB background: gravitational plane wave supported by constant null 5-form strength. We study $D3$ brane action in both covariant and light cone kappa symmetry gauges. Like the fundamental string action, the $D3$ brane action takes a simple form once written in the light cone kappa-symmetry gauge. We also consider the $\mathcal{N}=4$ SYM theory in 4d plane wave background. Since some (super)symmetries of plane wave SYM action are friendly to (super)symmetries of the type IIB superstring in plane wave Ramond-Ramond background we suggest this SYM model may be useful in the context of AdS/CFT duality. We develop the Hamiltonian light cone gauge formulation for this theory.