Alexander Markovich Polyakov

"We develop a for computing sums over random surfaces which arise in all problems containing (like , three-dimensional etc.). These sums are reduced to the exactly solvable quantum theory of the two-dimensional Liouville lagrangian. At D = 26 the string dynamics is that of harmonic oscillators as was predicted earlier by dual theorists, otherwise it is described by the nonlinear integrable theory."

"We have no better way of describing elementary particles than quantum field theory. A quantum field in general is an assembly of an infinite number of interacting harmonic oscillators. Excitations of such oscillators are associated with particles. The special importance of the harmonic oscillator follows from the fact that its excitation spectrum is additive, i.e. if E1 and E2 are energy levels above the ground state then E1 + E2 will be an energy level as well. It is precisely this property that we expect to be true for a system of elementary particles."

"can be understood in a very simple way by means of the Peierls argument. Namely, while the energy of the string is proportional to its length, the entropy of it also grows linearly (since the number of random curves grows exponentially with their lengths). Thus at a certain temperature the entropy takes over and infinitely long strings begin to dominate. That means liberation."

"Based at Princeton University, Polyakov was chosen from a shortlist of three, which included string theorist of the and a trio of researchers – of the , of the and of Stanford University. The shortlist and ultimate winner were chosen by a panel comprising nine physicists – seven of whom are string theorists and one a topological-insulator pioneer. Not surprisingly, string-theory naysayer of Columbia University is not pleased. “The [ceremony] was largely a string theory hype-fest…,” he wrote on his blog . Meanwhile in a very different dimension of the , Lubos Motl is elated and writes “Sasha Polyakov is a giant because he is a string-theory pioneer and because he has cracked many phenomena in gauge theories.” Motl also makes a confession of sorts about what he discovered while alone in Polyakov’s office…"

"Alexander Polyakov, a now at Princeton University, caught a glimpse of the future of in 1981. A range of mysteries, from the wiggling of strings to the binding of s into s, demanded a new mathematical tool whose silhouette he could just make out. ... In his paper he sketched out a formula that roughly described how to calculate averages of a wildly chaotic type of surface, the “.” His work brought physicists into a new mathematical arena, one essential for unlocking the behavior of theoretical objects called strings and building a simplified model of quantum gravity. Years of toil would lead Polyakov to breakthrough solutions for other theories in physics, but he never fully understood the mathematics behind the Liouville field. Over the last seven years, however, a group of mathematicians has done what many researchers thought impossible. In a trilogy of landmark publications, they have recast Polyakov’s formula using fully rigorous mathematical language and proved that the Liouville field flawlessly models the phenomena Polyakov thought it would."