What's the notion of negative amplitude? I hope the title and the question don't mean different things.
Sound is a pressure wave in a fluid medium. That medium has a "static"or average pressure and sound is simply a small change of that pressure (as a function of time). Negative sound pressure just means that the current pressure is a little lower than the average pressure.
For example, static air pressure is around 100,000 Pascals (Pa) . Normal audible sound is quite a bit smaller, maybe 0.1 Pa (for 76 dB SPL). That means that the pressure are the microphone (or your ear) varies from 99,999.1 Pa to 100,000.1 Pa
In a sound wave, troughs are regions of low (with respect to an average value) pressure, and, accordingly, low density. So, the answer to the title question, troughs are rarefactions.
The answer to the body of your question: the amplitude is always positive. But acoustic pressure level, a logarithmic measure of the effective pressure of a sound relative to a reference value, which is measured in decibels, can be negative. The reference value is the threshold of human hearing, which is given by ANSI standard as 20 uPa.