# Alexander Arkadyevich Migdal

Alexander Arkadyevich Migdal (Russian: Александр Арка́дьевич Мигдал; born 22 July 1945) is a Russian-American mathematical and theoretical physicist currently working at the Institute for Advanced Study in Princeton, New Jersey.

## Early life & education

Alexander Migdal was born in Moscow, Soviet Union in 1945, the son of prominent Soviet physicist Arkady Migdal and Tatiana Soboleva.
Migdal studied physics and mathematics as an undergraduate at Moscow Institute of Physics and Technology before receiving his PhD in theoretical physics from the Landau Institute for Theoretical Physics in 1969. He subsequently obtained his Doctor of Sciences (equivalent to the habilitation) and Professorship while at the Landau Institute.
Migdal defected with his family from the Soviet Union to the United States in 1988.

## Career

Alexander Migdal began his academic career as a researcher in theoretical physics at the Landau Institute upon receiving his PhD. He remained at Landau until 1984, when he decided to defect from the Soviet Union. Between 1984 and 1988, he worked at the Russian Space Research Institute while preparing to defect.
Migdal was unable to travel internationally starting in the 1970s, due to his unwillingness to cooperate with the KGB. As a result, his work prior to defection became less well known in the west than that of many contemporaries.
Following defection, Migdal spent the 1988 academic year at UC San Diego, before accepting a tenured professorship at Princeton University, with joint appointments to the departments of physics and applied mathematics.
Migdal left Princeton in 1996 to found Real Time Geometry, a pioneering developer of three-dimensional laser scanning. The company was subsequently acquired by ViewPoint Corp. in 1998, where Migdal spent several years as Chief Scientist. In 2000, he founded Magic Works, an early and successful algorithmic trading firm, remaining active there until 2011.
He returned to physics research in 2018 to complete work in turbulence that he began in 1993, joining the physics department of New York University as Research Professor with sponsorship from the Simons Foundation. From 2021 to 2023, he continued his physics research at NYU while simultaneously serving as Global Head of Research at ADIA, the sovereign wealth fund of Abu Dhabi in the United Arab Emirates.
Migdal returned to full-time research in physics at NYU in 2023, before joining the Institute for Advanced Study as a member in September, 2024.

## Scientific work

Migdal has made fundamental contributions to quantum field theory, quantum gravity and the study of turbulence.
As an undergraduate, Migdal and Alexander Polyakov worked out the theory of dynamical mass generation in gauge theories, now known as the Higgs mechanism, in late 1963, independently from Robert Brout, François Englert and Peter Higgs. This work ran counter to prevailing orthodoxy within the Soviet physics establishment, causing their paper, Spontaneous Breakdown of Strong Interaction Symmetry and Absence of Massless Particles, to be rejected by JETP in 1964 and 1965, before finally being accepted for publication in mid-1966.
Between 1967 and 1973, Migdal was active primarily in the area of critical phenomena and scale invariance and conformal field theory, beginning with his seminal paper from 1967 written with Vladimir Gribov connecting critical phenomena and quantum field theory. This work was subsequently developed by Migdal and Polyakov, working independently, into the Migdal-Polyakov conformal bootstrap, and was a precursor to the work for which Ken Wilson was awarded the Nobel Prize in 1982. The conformal bootstrap was further developed by Polyakov, Rychkov and others into what is now recognized as the preferred quantitative microscopic theory for understanding critical phenomena.
Migdal's work from 1974 to 1980 was focused on quantum chromodynamics, starting with a paper from 1975 in which he was first to establish how asymptotic freedom could lead to quark confinement by employing a novel form of the renormalization group. This work was popularized by Ken Wilson and Leo Kadanoff and later became known as the “Migdal-Kadanoff bond-moving approximation,” with lasting application in solid-state physics. In 1979, Migdal developed an exact relationship between quark confinement and asymptotic freedom in the form of a nonperturbative equation for the Wilson loop, in collaboration with his student, Yuri Makeenko. This equation is now widely used in quantum chromodynamics to study quark confinement.
In 1980, Migdal found that matrix models could be applied to topological quantum field theories such as quantum gravity. Initial results obtained in collaboration with Vladimir A. Kazakov showed that a triangulated planar matrix model was exactly equivalent to a continuum model. In collaboration with David Gross, Migdal further developed this work in a widely cited paper from 1990, providing the first exact solution for 2D quantum gravity. Edward Witten and others later expanded and generalized the applicability of matrix models to topological field theories.
In the early 1990s, Migdal began studying the application of ideas from quantum field theory to the theory of turbulence, deriving in 1993 an exact loop equation for velocity circulation within a fluid. Working with Gregory Falkovich, Victor Gurarie and Vladimir. V. Lebedev, he developed a description of intermittency in nonlinear systems by means of instanton solutions of the stochastic differential equations.
After a two-decade hiatus, in 2019 Dr. Migdal began publishing new research on various aspects of turbulence.