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Mikhail Shifman and Arkady Vainshtein |

Professors Mikahil Shifman and Arkady Vainshtein were awarded the International Center for Theoretical Physics (ICTP) 2016 Dirac Medal and Prize in Theoretical Physics. They were cited for their "contributions to a better understanding of field theories in the non-perturbative regime and in particular for exact results in supersymmetric field theories."

Perturbation theory is the standard method for approximating weakly coupled particles. It fails to describe strongly-coupled particles such as the quarks and gluons that make up protons, neutrons and other hadrons. Quarks and gluons remain locked inside hadrons at low energies and cannot be understood with perturbation theory. Many other basic properties of hadrons such as their masses are also non-perturbative.

The award citation described Shifman and Vainshtein’s collaboration, which began more than 40 years ago in Moscow, as one of the most fruitful in theoretical physics. “Among a variety of work on strongly interacting field theories, they introduced use of the gluon condensate (a property of the vacuum in QCD) and developed the Shifman-Vainshtein-Zakharov (SVZ) sum rules. The SVZ sum rules relate observed properties of hadrons to the gluon condensate and a few other condensates, sidestepping the issue of trying to calculate everything perturbatively from first principles.”

Shifman and Vainshtein also made fundamental contributions to the non-perturbative study of supersymmetric gauge theories (QCD itself is a non-supersymmetric gauge theory), culminating with the proposal of the Novikov-Shifman-Vainshtein-Zakharov (NSVZ) exact beta function in the 1980s. The beta function of a field theory describes how the coupling changes depending on the energy scale (for example, increased coupling at low energies is a key part of confinement). Expressions for beta functions are usually not exact, and instead are subject to corrections from higher order terms in perturbation theory.

Nathan Seiberg (Institute for Advanced Study, Princeton) was also awarded the medal. Seiberg was recognized for his discoveries in the field of supersymmetric gauge theories using a mathematical property of these theories—holomorphy—to understand non-renormalisation theorems (similar to the “exactness” just mentioned) and to decipher different ground states or vacua of N=1 supersymmetric theories (N indicates the number of supersymmetries present). He uncovered Seiberg duality, by which a strongly coupled theory is equivalent at low energies to a weakly coupled theory that may be built from a different set of fundamental particles. A theme of the work was to derive results in a weakly coupled theory where computations are simpler and then use the duality or holomorphy to carry the results across to a non-perturbative strongly coupled case. He has also made important contributions to string theory and other areas of theoretical physics.

In collaboration with Edward Witten (Institute for Advanced Study, Princeton; Dirac Medallist in 1985), Seiberg made major contributions toward a full non-perturbative understanding of N=2 supersymmetric gauge theories. The results of Seiberg and Witten unleashed a tremendous amount of further work, not only in theoretical physics but also in pure mathematics, where the insights provided astonishingly powerful methods to prove important theorems on topics such as four-dimensional manifolds.

ICTP's Dirac Medal, first awarded in 1985, is given in honour of P.A.M. Dirac, one of the greatest physicists of the 20th century and a staunch friend of the Centre. It is awarded annually on Dirac's birthday, 8 August, to scientists who have made significant contributions to theoretical physics.

Posted Friday, August 12th 2016
by Jenny Allan