The most important things in Svartulf Vargsson's life are family and faith. He is a highly loyal and dutiful young man, raised in a very close, very large, and very pious extended family. Svartulf dedicated to those close to him and to his family's patron deity—Thor [or this campaign's equivalent], god of thunder and favorite of the common man. Svartulf has a noble and honorable heart, and the heart of a warrior, but he does not seek fame as others who follow the way of the sword and the spear; he simply wishes to do right by his family, his ancestors, his people, and his god.
Thus, when Wulfgar comes to speak of Rothgar's plight, Svartulf will hardly need to be asked to fight; he will leap at the chance. There is a debt to Rothgar's family that Svartulf's line must repay, and Svartulf is happy to repay it, especially if doing so would also honor his beloved Thor, hero god and giant-slayer. Svartulf's great-grandfather, Eyjarr Galmannson, you see, was once owned by Rothgar's grandfather—he was a slave, laborer and servant.
The story goes that Rothgar's ancestor treated Svartulf's with kindness and grace, and that before either perished, Eyjarr was released from service, granted the rights of a free man that his descendents have enjoyed. Rothgar and Wulfgar, to be certain, will not know the name of Eyjarr Galmannson—but Eyjarr remembered Rothgar's grandfather for all his life. He told the tale many a time of the nobleman who gave his family a chance to be free to his son, Gangulf Eyjarsson, who told the tale to his son, Vargr Gangulfson, who told the tale to his son, Svartulf Vargsson, who will finally give to Rothgar what is owed.
[Mechanically, Svartulf will be a Weapon Master focused on the warhammer, of course, what with it being Thor(or this campaign's equivalent to Thor)'s favored weapon.]