One of the connections that exists between the real world and the world of the fairies in Yeats's "Stolen Child" is the pain and suffering that makes leaving it quite inviting.
The real world and the world of the fairies are opposites. The fairies represent a world that is idyllic and filled with the splendor of the "leafy island," "moonlight glosses," and "further Rosses." "Water bubbles" and "frothy gushes" dot the landscape. The world of the fairies is filled with creatures in their natural habitat, such as "slumbering trout," "flapping herons," and "ferns that drop their tears over the young streams." This world is lush and pure. Its description is alluring.
Leaving the real world that Yeats depicts might not be such a bad thing. The real world is shown to be undesirable: "the world is full of troubles/ And is anxious in its sleep." The closing line to each stanza also confirms this: "...the world's more full of weeping than you can understand." If the child stays in this real world, its negativity will rob him of joy. As the fairies take the boy, they note that he is "solemn-eyed." This might be a reflection of how the real world is already taking its toll on the child.
The reader observes both worlds. The world of the fairies is one of bliss, while the real world is one of pain. It is significant that a child is poised between both. On some level, childhood innocence is the first casualty of maturation. The child being "stolen" might be the only way his innocence can be preserved. It is stolen back from the ravages of a real world that invariably corrupts that which it touches. This is where the poem displays a connection between the real world and the world of the fairies.