Slavery is the belief that humans can be owned as property.
I suppose if property ownership is part of capitalism, then they have this slight connection, as communism is the abolishment of property ownership, and therefore, slavery would be impossible under communism.
The usual argument is that slavery is not market-efficient in an industrial economy, and, on the other hand, capitalism inevitably leads to an industrial economy, thus killing slavery in the process.
The introduction of the mechanical cotton gin induced a very sharp rise in demand for slave labor in the American South. Mechanizing the processing of cotton created an increased demand for picking cotton, a process which had not yet been mechanized.
Maybe if people had waited a few more years for the mechanization of cotton picking, this would have corrected itself. Or maybe not. Maybe further mechanization would have created other opportunities for the use of slave labor.
My point is, "more industry = less slavery" is an oversimplification.
Slavery is the belief that humans can be owned as property.
I suppose if property ownership is part of capitalism, then they have this slight connection, as communism is the abolishment of property ownership, and therefore, slavery would be impossible under communism.