String Theory and Umbral Moonshine

Don't Let The Name Fool You!

The mathematical terms you are about to read are going to sound bizarre, but please keep in mind that most new physics and math terms sound bizarre at first. Think about it, we live in a world of charm quarks, imaginary numbers, strange attractors, quasars and nebula. So when you're reading the article I'm passing along below, and you come across the terms Moonshine and Umbral Moonshine, just remember that these are mathematical objects that people will take for granted in the future just as we take for granted the terms transcendental numbers and manifolds.

String Theory As a Mathematical Bridge

Ok, so there are some interesting things happening in mathematics right now. In a paper recently posted to archiv.org, some mathematicians have presented a numerical proof of the Umbral Moonshine Conjecture. It is important for many reasons including that a greater understanding (and proof) of this conjecture could go a long way in helping physicists combine general relativity and quantum mechanics convincingly through string theory.

Here is a quick wikipedia link that describes Moonshine.

Below is a Scientific American article on the recent arxiv.org paper and its implications in this areas of mathematics and physics. Enjoy!

Mathematicians Chase Moonshine's Shadow

In 1978, the mathematician John McKay noticed what seemed like an odd coincidence. He had been studying the different ways of representing the structure of a mysterious entity called the monster group, a gargantuan algebraic object that, mathematicians believed, captured a new kind of symmetry. Mathematicians weren't sure that the monster group actually existed, but they knew that if it did exist, it acted in special ways in particular dimensions, the first two of which were 1 and 196,883. McKay, of Concordia University in Montreal, happened to pick up a mathematics paper in a completely different field, involving something called the j-function, one of the most fundamental objects in number theory. Strangely enough, this function's first important coefficient is 196,884, which McKay instantly recognized as the sum of the monster's first two special dimensions.

Most mathematicians dismissed the finding as a fluke, since there was no reason to expect the monster and the j-function to be even remotely related. However, the connection caught the attention of John Thompson, a Fields medalist now at the University of Florida in Gainesville, who made an additional discovery. The j-function's second coefficient, 21,493,760, is the sum of the first three special dimensions of the monster: 1 + 196,883 + 21,296,876. It seemed as if the j-function was somehow controlling the structure of the elusive monster group.Soon, two other mathematicians had demonstrated so many of these numerical relationships that it no longer seemed possible that they were mere coincidences. In a 1979 paper called "Monstrous Moonshine," the pair-John Conway, now of Princeton University, and Simon Norton-conjectured that these relationships must result from some deep connection between the monster group and the j-function. "They called it moonshine because it appeared so far-fetched," said Don Zagier, a director of the Max Planck Institute for Mathematics in Bonn, Germany. "They were such wild ideas that it seemed like wishful thinking to imagine anyone could ever prove them."

Article Continues Here