# Grand unified theory

Mathematical quest

It allows us to do computations, impossible before the advent of string theory

MSI mathematician Professor Peter Bouwknegt is on the trail of the holy grail of physics – a theory of everything unifying quantum mechanics and Einstein’s general theory of relativity. He’s developing new mathematics needed to formulate string theory, seen as the only path to a theory joining the physics of the subatomic realm and the description of space and time on the cosmological scale.

A theory of everything unifying the four forces – the weak and strong nuclear forces, the electromagnetic force and gravitation has eluded mathematicians and physicists for decades.

String theory treats the fundamental units of matter – the elementary particles such as the electron, photon and graviton – as resonances, or excitations of a one-dimensional string, like a note on a guitar string.

Bouwknegt has been deploying various mathematical tools, including differential geometry and algebraic topology, to describe the symmetries of string theory for over ten years.

“Symmetries are critically important to physical modelling because they relate the outcomes of experiments for different observers, and constrain the number of possible models one could potentially write down.” he says. “The mathematical modelling of those symmetries has led to many important advances, most notably the theory of groups and algebras.”

Apart from the familiar symmetries such as Lorentz invariance, which relates observers in different reference frames, string theory has some peculiar symmetries known as dualities. These are less well understood and their description requires new mathematics.

“They have profound consequences and are the reason why string theory is not only very powerful but also quite robust,” Bouwknegt explains. “For instance, S-duality relates strong and weakly coupled string theories. It allows us to do computations, impossible before the advent of string theory, in a strongly coupled system, such as a black hole, in terms of a dual weakly coupled system.”