Delay, retard, slow, slacken, detain are not always close synonyms, but they carry the same basic meaning: to cause someone or something to be behind in his or its schedule or usual rate of movement or progress.
Delay implies the operation, usually the interference, of something that keeps back or impedes, especially from completion or arrival at a set or given time.
Retard applies especially to motion, movement, or progress and implies something which causes it to reduce its speed.
Slow (often followed by up or down) and slacken also imply a reduction in speed or rate of progress, but slow usually implies deliberation or intention and slacken, an easing or letting up or a relaxation of some sort.
Detain (see also ARREST 2) implies a being held back beyond an appointed time, often with resulting delay in arrival or departure or in accomplishment of what one has in mind.