D-branes in PP-Waves and Massive Theories on Worldsheet with Boundary

TL;DR

This paper explores supersymmetric D-brane configurations in pp-wave backgrounds, classifying A-type and B-type branes based on their geometric properties and analyzing their supersymmetry preservation and gauge field excitations.

Contribution

It provides a detailed classification of supersymmetric D-branes in specific pp-wave backgrounds, including the effects of gauge fields and backgrounds with different supersymmetries.

Findings

A-type branes wrap special Lagrangian submanifolds with constant imaginary superpotential.

B-type branes wrap complex submanifolds with constant superpotential.

Inclusion of gauge fields yields BPS D-branes with gauge excitations.

Abstract

We investigate the supersymmetric D-brane configurations in the pp-wave backgrounds proposed by Maldacena and Maoz. We study the surviving supersymmetry in a D-brane configuration from the worldvolume point of view. When we restrict ourselves to the background with N=(2,2) supersymmetry and no holomorphic Killing vector term, there are two types of supersymmetric D-branes: A-type and B-type. An A-type brane is wrapped on a special Lagrangian submanifold, and the imaginary part of the superpotential should be constant on its worldvolume. On the other hand, a B-type brane is wrapped on a complex submanifold, and the superpotential should be constant on its worldvolume. The results are almost consistent with the worldsheet theory in the lightcone gauge. The inclusion of gauge fields is also discussed and found BPS D-branes with the gauge field excitations. Furthermore, we consider the backgrounds with holomorphic Killing vector terms and N=(1,1) supersymmetric backgrounds.