Absolute NU is completely indifferent to happiness (over and above any merely instrumental effects it has on reducing suffering). Suppose there were a world that consisted of a thriving utopia, filled with love, excitement, and joy of the highest degree, with no trace of suffering. One day this world is at threat of losing almost all of its happiness. If this threat comes to pass, almost all the happiness of this world will be extinguished. To borrow from Parfit’s memorable example, they will be reduced to a state where their only mild pleasures will be listening to muzak and eating potatoes. You alone have the power to decide whether this threat comes to pass. As an Absolute Negative Utilitarian, you are indifferent between these outcomes, so you decide arbitrarily to have it lose almost all of its overflowing happiness and be reduced to the world of muzak and potatoes.
Here is a classic piece on the subject by Toby. Brief quote from one line of argument:
And the excellent Point-by-point critique of Ord’s “Why I’m Not a Negative Utilitarian” by Magnus Vinding.