In Act I, in "the battle" who does Macbeth fight against? Does the Thane of Cawdor side with the King of Norway or Macdonwald?

In Act I, scene 2 of Macbeth, both Macdonwald and the thane of Cawdor are traitors against Scotland, while Macbeth is a hero fighting for Scotland. The reader learns that "The merciless Macdonwald-- Worthy to be a rebel" was fighting against Macbeth, who defeated him. Therefore, Macdonwald was a traitor to Scotland. As the sergeant says, "but all's too weak:/ For brave Macbeth." Macbeth, the Scottish hero, treats his rebellious enemy, who has deserted the Scottish side, with no pity. Instead, "he unseam'd him from the nave to the chaps,/ And fix'd his head upon our battlements." In other words, Macbeth sliced off the head of the the rebel Macdonwald and placed it on the top of the wall. For his bravery in battle, Duncan, the king, rewards Macbeth with the title thane of Cawdor at the end of this scene.

Ross appears to tell the king that the thane of Cawdor has, like Macdonwald, been a traitor in the battle between Scotland and Norway: "Norway himself,/ With terrible numbers,/ Assisted by that most disloyal traitor/The thane of Cawdor, began a dismal conflict." For this reason, Duncan tells Ross to have the thane of Cawdor killed. Duncan says, "No more that thane of Cawdor shall deceive/ Our bosom interest: go pronounce his present death,/ And with his former title greet Macbeth." In other words, the thane of Cawdor will be killed for being a traitor, and his title will pass to Macbeth. This is the honor that Macbeth receives at the beginning of the play, and it makes him hungry for more power.