What story does Oath of the Horatii depict?

Jacques-Louis David's 1785 painting Oath of the Horatii depicts a scene from Roman legend recorded by the historian Livy. The story concerns a conflict between Rome and Alba Longa around 669 BCE, which was to be settled by combat between two sets of triplet brothers: the Roman Horatii and the Alban Curiatii.123

The painting captures the moment the Horatii brothers swear to fight for Rome, choosing political duty over personal ties. This choice is particularly poignant because the families are intertwined: one Horatii sister is betrothed to a Curiatii brother, and a woman from the Curiatii family is married to one of the Horatii. Despite the lamentations of their grief-stricken sisters, the brothers obey their father’s exhortation to fight. Notably, while the painting is famous for this dramatic oath, there is no mention of such an oath in Livy’s original account.123