Any type of historian could study the institution of slavery in the United States, and most historians (and most histories) don't fall neatly into a single category.

An economic historian might look at the working conditions and larger economic impacts of the system of chattel slavery. Was slavery a sustainable economic system, or was it destined to collapse under its own weight? Who benefited from the slave trade, and how did the accumulation of wealth from this practice impact the history of the United States and the world?

A military historian might look at how slavery impacted major conflicts throughout history. What role did enslaved people played in the American Revolution? How did the Union's policy of declaring slaves to be "contraband" during the Civil War affect the course of the war?

A cultural historian might study the arts and culture of enslaved people. What chance did they have to make art? What were their customs, rituals, and religion? Where did these practices originate and how did they spread? What is the legacy of this art or these customs?

A social historian might seek to understand the everyday lives of enslaved people. How did the institution of slavery affect their daily lives? What did they eat? How did they live, love, and build families? How did slavery affect their faith? How did they feel about the condition of their life, and how do we know?

The list goes on and on.

I'm not aware of any single field that would be considered "U.S. slavery studies", but there are any number of ways to tackle this complex topic. If you're hoping for a more holistic approach to the topic, many universities have African American Studies programs that, by necessity, must deal with the legacy of American slavery and do so in a way that considers many of these issues in an interdisciplinary way.