Here is some information about my academic and industrial achievements.

I started very early, as an undergraduate student at FizTech. I am quite proud of my second paper, where my best friend Sasha Polyakov and I discovered the dynamical mechanism of symmetry breaking and mass generation in Gauge Theory in 1964, independently of Higgs, Englert, and Brout. The conservative Landau School fiercely opposed us, causing our paper to be rejected twice in JETP and finally published only in 1966. Although we cannot claim credit for this discovery due to the delay, we can be satisfied that we stood against retrogrades and fought for the truth we discovered.

My next notable paper was my work with Vladimir Gribov in 1967-68, where we discovered anomalous dimensions in scale-invariant field theory. I later applied this, parallel to similar work by Sasha Polyakov, to the critical phenomena in statistical physics.

Our pass was taken by Kenneth Wilson, who achieved the goal of a quantitative theory of phase transitions by applying the renormalization group and his $\epsilon$ expansion. Still, we had the last word: the conformal bootstrap we discovered was advanced in this century into a quantitative theory by Rychkov, which computes both the indexes and correlation functions.

I worked with Gribov for a few years on his Reggeon Field Theory, which was technically advanced but became obsolete after the discovery of Asymptotic Freedom by Gross, Wilczek, and Politzer. I then dove into QCD – The Theory of Strong Interactions.

I discovered quark-resonance duality, which led to the QCD sum rules of Shifman, Wainshtein, and Zakharov. I was still working on this theory just two years ago, merging ideas from CFT and String theory, and explaining some mysterious relations between my phenomenological QCD spectrum from the ’70s and the remarkable AdS-CFT analogy discovered in the last decades. Remarkably, my phenomenological formulas, relating the string mass spectrum to the spectrum of dimensions of CFT as roots and indexes of Bessel functions, were rediscovered 30 years later in the context of AdS-CFT duality.

I worked for many years in the field of Large N QCD and Quantum Gravity, establishing analogies between QCD and String theory. Notable achievements include the Loop Equation in Large N QCD, which reduced field theory to a nonlinear 1D problem of loop dynamics.

Another exciting project was the exact solution of 2D Quantum Gravity, which began with a series of papers with Volodya Kazakov and was completed with help from David Gross, Edouard Brezin, Shenker, and Douglas.

In the ’90s, my work mostly involved technical advances, such as Loop Equations in Turbulence, where I reduced the 3D field theory of decaying turbulence to a nonlinear stochastic 1D ODE. This equation can solve the large-dimension limit of Turbulence. Unfortunately, I never finished that work.

Nor did I complete my work on the algebraic formulation of the QCD momentum loop equation. It opened the way to an exact solution in the infrared limit, which I never found.

The Wind of Fate led me to a new life in Industry as an Inventor and Entrepreneur. I started an Internet startup in the mid-’90s with a couple of students. A year later, I sold the company to a public company and left academia for good (or so I thought). It was a stressful life, but I never regretted quitting my beloved Princeton University.

Throughout my academic career, I mostly generated ideas, but in my industrial career, I had to develop and implement my ideas into working products and technologies. These technologies made it into Windows 98, AOL7, Minolta 3D camera, Lockheed-Martin RealScan3D, and other products. I founded a public company and served as Vice Chairman and Chief Scientist until March 2000, when I left to work on a stock trading system. I did this for almost 20 years, with intermittent success but unwavering enthusiasm.

But the Wind of Fate was not finished with me. In 2019, quite accidentally, I learned that my old friend Katepalli Sreenivasan (Sreeni) completed a large project he started in the ’90s: numerical simulations of Turbulence where he specifically measured the velocity circulation I studied theoretically in 1993 in my Loop Equations.

I predicted the Area Law – the probability distribution for the circulation over a large loop in the turbulent flow depends on the minimal surface bounded by this loop and obeys a universal scaling law.

This prediction went against all the existing theories (or, more accurately, models) of Turbulence in the previous century. Experts shrugged my theory off as the Higgs effect and matrix models of 2D Gravity had been. Experts returned to their models, and I quit to go to Industry, where you do not need to prove anything as long as your system works.

But Sreeni was persistent: he overcame the objections of the conservative Turbulent community, finished his project, and published his paper. He confirmed my predictions!

The moment I learned that, my life changed again. I dropped my financial career—no amount of money can substitute the joy of scientific discovery. Besides, I was never good at making money. It’s one thing to predict the market (which is predictable, to a large extent) and another to create a profitable trading system—there are too many business elements for which I have no talent.

As Pushkin wrote in his “Revival”:

Like this, the darkly apparitions
Are leaving off my tortured heart,
And it again revives the visions
Of virgin days I left behind.

— Alexander Pushkin, translated by Yevgeny Bonver

I turned my back on the stock market, applied for the Simons Foundation grant, and got a job as a Research Professor at NYU in October 2019. Since then, I have published seven papers on arXiv, and on my 75th birthday, I submitted the eighth paper, summarizing and advancing my new theory.

I had to catch up with Mathematical Physics, which evolved during the 25 years I was away. To my surprise, though, Turbulence theory was stagnant – everybody was still hypnotized by the Kolmogorov model of 1941.

I had some beginner’s luck, or rather, I had the advantage of a fresh perspective. The advances made in Gauge Theories over the last 25 years were quite applicable to Turbulence, so I used analogies of gauge invariance, instantons, and confinement in my new theory.

After inevitable trial and error, I arrived at a novel formulation of the Field Theory of Turbulence (let us cautiously call it a new model), which goes much further than my Loop Equations. It predicts the shape of circulation distribution, in perfect agreement with Sreeni’s measurements.

There are many more things to do in this new theory, both theoretically and in numerical simulations. I am actively collaborating with Sreeni and his postdoc, Kartik Iyer.

Harmony and happiness have returned to my life. Like Faustus, I can now say: “Beautiful moment, do not pass away!” Let us hope that Mephistopheles does not rush to collect his debts from me…

P.S. (2021)  Now, with more than a dozen papers published on Turbulence, I may be approaching the final stretch. The theory of vortex surfaces, which I have been developing for many years, is close to completion. Then I may get bored again.

I am not done with the stock market yet! Some ideas work in theory, but I could not implement them with limited resources at my company. These ideas would only work globally, with hundreds of thousands of financial instruments traded across all markets. If the Wind of Fate calls me again, I may not resist the temptation…

P.P.S. (2024) The Wind of Fate swept me to Saadiyat Island in the Persian Gulf, near Abu Dhabi. As Kurt Vonnegut said, “peculiar travel suggestions are dancing lessons from God.”

I was seduced into becoming the Global Head of Research at ADIA, the Hedge Fund that manages $850 billion of the personal wealth of the Sheikhs of Abu Dhabi.

Instead of simply saying no to this idiotic offer, I demanded an insane salary plus the freedom to work on Turbulence half-time.

As often happens in negotiations, genuine reluctance only raised the stakes, so my impossible wish was granted. The rich life in Abu Dhabi lasted for two years, after which I became so engrossed in my work on Turbulence that the General Manager Majed offered to part ways as friends, which I did with a sigh of relief.

The thing is, I DID it!

Finally, in 2022-23, I found exact analytic solutions to my loop equations for decaying turbulence. Initially, it looked too abstract and exotic, but I checked and re-checked—and there was no doubt—that the solution I found satisfied the Navier-Stokes loop equations.

The most surprising result was that this solution reduced classical hydrodynamic turbulence to a one-dimensional Fermi quantum system. This is an example of so-called duality, which sometimes occurs in quantum theory. A famous recent example is a duality between Conformal Field Theory and some quantum gravity in anti-DeSitter space. This discovery made Juan Maldacena one of the most famous living theorists.

In my case, there appeared to be an even more amazing duality between classical turbulence and quantum mechanics. I could not think about any financial problems until I had worked out all the consequences of my duality. This one-dimensional model with fermions on a ring turned out to be exactly solvable, as they say, in quadrature.

The observable quantities—the decaying energy as a function of time, the whole energy spectrum of decaying turbulence—were reduced to integrals of transcendental functions related to Number theory.

In particular, I computed the spectrum of decay indexes for various quantities—energy spectrum, velocity correlation function, etc. The spectrum appeared to be related to the complex zeros of the Riemann zeta function, one of the last mysteries of number theory.

But the best part of this dramatic story is that my theory perfectly fits the available experimental data and the so-called DNS (numerical simulation of the Navier-Stokes equation).

These experimental data, which I learned to process to minimize statistical errors, revealed a shocking truth.

The Kolmogorov scaling laws in decaying turbulence were a myth!

The precise experimental and DNS data I have fitted perfectly agree with my theory and completely rule out the famous K41 laws, which were accepted (without any microscopic justification) as a basis for theories of turbulence.

The old data either had too large errors or were never fitted properly across a wide range of scales, but there is no doubt now– K41 laws are wrong.

Look at this plot of the effective index for the correlation function of the velocity field as a function of , where is the effective length scale at a given time t of the decay.

In my theory, .

The red dots on this plot represent the DNS data; the green line (my theory) goes straight through this data.

The K41 “law” corresponds to the constant value 2/3, plotted as a blue dashed line. Not even close!

The emperor has no clothes.

The size of the lattice used for DNS by Sreeni and collaborators in 2023 was just 1024. Such simulations could have been performed thirty years ago—nobody cared back then.

Several researchers suspected this, but eighty years of repetition hypnotized five generations of researchers, so nobody openly said so until now.

I have given numerous talks about this theory all over the world. I do not hear any scientific objections, but I do not hear any admissions either. Everybody waits until someone else reproduces and compares my calculations with new experiments.

 

Here is my online guide to this work on the quantum solution of classical turbulence.

https://sashamigdal.github.io/QuantumSolution/

Life has suddenly become very exciting…