I think the largest carnivore would be the Sperm Whale.

I would say, on average, that Polar bears are the largest bear. That's the laws of nature, the furtherest a typical species is away from the equator, the larger it has to be in order to survive (has to do with body surface area in relation to weight). That is why most species of people that live near the equator are generally small and thinner but the Vikings and others nearer the poles are generally larger genetically.