Supersymmetric objects in the M-theory on a pp-wave

TL;DR

This paper systematically derives all classical BPS equations in M-theory on a pp-wave, classifies supersymmetric solutions, and explores how rotating fuzzy spheres affect supersymmetry preservation.

Contribution

It provides a complete classification of classical BPS equations and solutions in M-theory on a pp-wave, revealing the structure of supersymmetry breaking and unique solution sets.

Findings

Classified BPS equations for different fractions of preserved supersymmetry.

Identified unique and inequivalent types of BPS solutions.

Showed how rotation affects supersymmetry preservation levels.

Abstract

We obtain, in a systematic way, all the classical BPS equations which correspond to the quantum BPS states in the M-theory on a fully supersymmetric pp-wave. The superalgebra of the M-theory matrix model shows that the BPS states always preserve pairs of supersymmetry, implying the possible fractions of the unbroken supersymmetry as 2/16, 4/16, 6/16,.... We study their classical counterparts, and find there are essentially one unique set of 2/16 BPS equations, three inequivalent types of 4/16 BPS equations, and three inequivalent types of 8/16 BPS equations only, in addition to the 16/16 static fuzzy sphere. We discuss various supersymmetric objects as solutions. In particular, when the fuzzy sphere rotates, the supersymmetry is further broken as 16/16 -> 8/16 -> 4/16.