In chapter 6, what is the correlation between what is going on in the "real world" and what is happening on the island?
I think what the question is implying is about the atomic war that the book takes place in. But this was a question designated for chapter 6 which didn't really go into much detail about it or anything.
What happens at the beginning of chapter six is essential to making the connection between what is going on in the "real world" and what is happening on the island. You're right in that it has to do with the atomic war going on - the chapter begins with the mention of an airplane fight 10 miles overhead. The lights from this battle can be seen, but no noise reaches the island.
What does reach the island, though, is very important. Golding writes that "a sign came down from the world of grown-ups.... There was a sudden bright explosion and corkscrew trail across the sky; then darkness again and stars. There was a speck above the island, a figure dropping swiftly beneath a parachute, a figure that hung with dangling limbs."
A dead fighter pilot with his parachute drifts to the island, and the breeze drags him up the mountain, until he stops "huddled among the shattered rocks of the mountain-top." Here, he is tangled up in his lines, and "when the breeze blew, the lines would strain taut and some accident of this pull lifted the head and chest upright so that the figure seemed to peer across the brow of the mountain. Then, each time the wind dropped, the lines would slacken and the figure bow forward again, sinking its head between its knees." When the boys tending the campfire later see this, they believe it is a beast, and soon, after Ralph, Jack, and Roger climb the mountain and see the same inexplicable figure, the older boys give in to the fear that before, only the littluns had of a "beast" on the island. Once this fear takes over, chaos ensues.
Besides this real world/island connection involving the "beast," the war overhead mirrors the fighting that is occurring between the boys on the island as they takes sides and separate into two camps: the one led by Ralph and the other by Jack. This "war" will only escalate in the coming chapters.