Prof. Cumrun Vafa

From Baagh-e Vafa to Harvard
Prof. Cumrun Vafa; an Intimate Profile
 

Legend has it that an apple fall on Newton’s head inspired him to formulate the laws of gravity. Regardless of the truth behind it, this is more a story of being curious than a story of being lucky. As Albert Einstein once said, “The important thing is not to stop questioning. Curiosity has its own reason for existence.” After all, such a moment has probably happened to everybody as it happened to Cumrun Vafa, Hollis Professor of Mathematicks and Natural Philosophy at Harvard University. “When I was 7 or 8 years old, I was wondering why the moon doesn’t fall on the ground,” he remembers.

No one answered the question for him, but he says that was not important. “What bothered me was not that I couldn’t get a good answer but that it didn’t bother anyone else.” Perhaps, because of his appreciation for wonderer spirits, Vafa decided to donate the monetary award of Mustafa Prize to help those who do bother by such questions. He asked the Mustafa Science and Technology Foundation (MSTF) to direct the entire financial reward of his prize to form the seed fund to create an International Research Institute for Fundamental Physics located in Iran.

He, of course, is one of the few who kept his sense of curiosity and wonder alive all through his life. He never stopped asking hard questions about the nature of the universe and remained curious as he was in childhood. “Where do we come from? What are the fundamental laws of nature? What is everything made of? Can we have a simple description of everything? These are the kind of questions which drew me to science,” he says.

Now, in the fourth decade of his career, Vafa is wrestling with the most challenging questions about the foundations of reality, questions about the nature of gravity and matter at the most fundamental level. Somehow, as a leading string theorist, he is still pursuing his childhood questions about moon with an approach that also has roots in his childhood and early education.

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Vafa vividly remembers when his teacher, Mrs. Sadighi, taught them the concepts of height, width, and depth for the first time in the third grade in primary school. “I remember asking myself why do we have exactly three of these things? Why not more or less than three? In other words, in my primitive way, I was wondering why the space is three-dimensional.” It seems just three dimensions were never enough for Vafa, neither in childhood nor now. Many years later, he just happened to be the founder of F-theory, a branch of string theory with 12 dimensions.

The most critical feature of the F-theory is its geometrical language that turned it into a very powerful framework. F-theory helped researchers to describe everything very geometrically. It seems the geometry is Vafa’s personal niche, a hometown that he knows all its backdoors and shortcuts. Beginning in high school, he got really excited about studying geometry. The idea that simple logical deduction from Euclidean axioms can shed light on the properties of circles and triangles was satisfying for him. “That one could draw an auxiliary line to solve an otherwise difficult geometry problem was like a fun game to play. I had a lot of pleasant hours with my friends in high school where we spent on proving geometry statements,” he says. However, as a high school student, he never thought of his future as a scientist. “At the time, trying to become a scientist was not viewed as a very ambitious career objective! It was only later, in university, where my love for science led me to decide to focus on mathematics and physics and finally in graduate work mainly on physics,” he says.

Vafa’s enthusiasm for science came about in the early years of his high school education when he saw one of his cousins doing his physics in the last year of high school. “He was doing calculations on a piece of paper, and I asked him what he was trying to accomplish. He explained to me that by the calculation, he is trying to find out if you throw a ball in the air at a given angle with a given speed where it will hit the ground,” he remembers. He was shocked that it was possible to use mathematics to answer such a question. That one can predict what will happen to things moving around us by logical reasoning. “This connection between pure thought, in the form of mathematics, and its application in explaining reality was what made a long-lasting impression in my mind,” he says.

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Vafa attended the prestigious Alborz High School in Tehran. It was the part of his life that his associates had a significant role in the path he finally chose for his career. “Alborz high school classmates, Principal, Dr. Mojtahedi, and other teachers had an important influence on me as I grew up while learning new subjects,” he says.

Vafa is world-renowned for his groundbreaking works in string theory and the mathematical technology needed to explore this field. He is one of the founders of the duality revolution in string theory, which has reshaped our understanding of the universe’s fundamental laws.

However, reaching such a position needs more than just curiosity and passion. Vafa always has been a hardworking person. Later in high school, he started to study his own aspects of Maxwell’s theory of electricity and magnetism. Then he studied Einstein’s theory of special relativity which he found beyond belief at the time. “Phenomena predicted by Einstein’s theory, such as contraction of lengths or dilation of time, were, on the one hand, mind-boggling and on the other quite magical,” he says. In fact, many of the ideas of special relativity could be illustrated using Euclidean geometry. Those fascinating thoughts played very nicely with his enthusiasm for geometry.

In 1977 Vafa went to the USA as an undergraduate at the Massachusetts Institute of Technology (MIT), where he got his bachelor’s degree in math and physics as a double major. For graduate work, he went to Princeton, where he earned his Ph.D. in Physics in 1985. He then became a junior fellow at Harvard, where he has been a professor of physics for more than three decades. In 2018, he was officially appointed the Hollis Professor of Mathematicks and Natural Philosophy in the Physics Department at Harvard University. This endowed professorship, established in 1712, is the second oldest chair at Harvard and the oldest chair in science in all of the United States. Vafa is the 15th incumbent of the chair through its history of more than 300 years.

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Vafa enjoys art, music, poetry, culture, and philosophy when he is not doing physics. “Listening to music and especially Persian music is very relaxing and inspiring for me,” he says. His daily swim is also a source of balance for him as an occasion to float freely as if in outer space and think freely about everything or maybe a “theory of everything.” However, he says, above all, he enjoys spending time with his family and friends. He believes humanity, kindness, and bonds with his family and friends are those aspects of life he cherishes most. “I was fortunate to be living in a family compound in Shemiran, surrounded by relatives, nature, tall trees, and a peaceful environment. I remember the interesting stories my grandmother would share with us while running around in our compound – Baagh-e Vafa. The beautiful sight of the Alborz Mountain is imprinted in my mind from my viewing of it when I was a child, and thinking of it still brings back good memories,” he says. “I have been very fortunate to have had a very happy childhood. Raised by kind and caring parents, with two protective and fun brothers, one older and one younger.”

Vafa believes many people, from his parents to and friends to his teachers and professors played key roles in his life and career. “But perhaps, if I were to single out one person, it would be my wife, Afarin Sadr, who has had the most impact on who I am today. And of course, our children - Farzan, Keyon, and Neekon - who have been an inspiration for me.”

One to Rule Them All
How Prof. Cumrun Vafa and other string theorists are pushing the boundaries of physics to the limit in pursuing the Einstein dream

Einstein spent the last four decades of his life pursuing the dream of uniting the general theory of relativity with quantum mechanics without any success. "The intellect seeking after an integrated theory cannot rest content with the assumption that there exist two distinct fields totally independent of each other by their nature," He said in his Nobel lecture in 1923.

The dream has been the Holy Grail of physics, an 'everything theory' or 'final theory' as some physicists prefer, that brings all the foundations of physics under one umbrella. However, today more or less, the situation is as was, but many physicists believe now they know the right approach: string theory. "This is the only theory which has resolved the inconsistency of .Einstein's theory of general relativity with the microscopic world of quantum mechanics," Cumran Vafa says

Vafa, a leading physicist world-renowned for his groundbreaking works in string theory, has pursued the dream just as long as Einstein did. "I have worked on string theory beginning in my graduate studies in Princeton University in the mid-1980s, and I have continued it non-stop till today," he says. He believes string theory is "the most fundamental theory of the universe. Whether it is the `final theory' or even that there is a `final theory' at all, remains to be seen".

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2500 years ago, the Greek philosopher Empedocles in his great work, On Nature, postulated that everything is composed of four elements: earth, water, air, and fire. He believed these elements or roots, as he said, are moved by two opposing forces; love and strife. Everything was explained by the four elements and two forces back then. How cool was that? However, it seems that was the last time we had a theory of everything.

The theory did not last much, and only one century later, it could not explain the variety of elementary substances found by alchemists. The pursuit for elementary substances went on to the point that in the eighteen-century chemists drew a table of near 100 elements. However, by discovering the atom and its internal structure, the modern age of reductionism began.

At the end of the nineteenth century, physicists developed quantum mechanics to explain why atoms absorb and emit light only by specific wavelengths. Then, Einstein came up with special relativity to combine space and time in 1905. A decade later, he introduced general relativity to merge special relativity with gravity. Trying to remove the contradiction between quantum mechanics and special relativity led to the successful quantization of electrodynamics.

By the emergence of particle colliders with high energy enough to probe the nuclear force, physicists opened up the gate of a subatomic particle zoo, which was a minor drawback. However, they soon realized most of the particles were composite, made up of 25 elementary particles ruled by three fundamental interactions: electromagnetic, weak nuclear, and strong nuclear. The unification was on fire.

The real climax was when physicists successfully merged the weak nuclear force, responsible for radioactive decay, with electromagnetism through a glamorous unification called electroweak interaction. The unification was so brilliant that all were convinced the next reasonable step should be a grand unified theory (GUT) consisting of all three fundamental interactions.

Through all those victorious years till now, the general relativity has been an almighty nuisance. The theory refuses to consistently combine with the standard model of elementary particles. In the last 80 years, physicists couldn't even develop a quantized version of gravity, let alone merge it with other fundamental interactions to make a theory of everything. Now, at the bottommost of the foundations of physics, we have two extremely successful but contrary theories: the standard model describing the microscopic world and the general relativity describing the universe at the largest scales.

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String theory was initially developed to describe the strong nuclear interaction, but another theory - quantum chromodynamics – did the job perfectly. In the mid-1970s, physicists noticed that the strings, despite the inglorious birth, have an exciting feature resembling an exchanging force just like gravity. So the strings were revived as a promising idea for a theory of everything.

String theory "postulates that the basic entities of matter are not just point-like particles like electrons, but also extended objects like strings," Vafa says. However, the string-like substructures have to inhabit a world that has way more than three dimensions. Do not look around for those extra dimensions; they are of a finite size or so "compactified" we cannot see them. For mathematical consistency, early string theories required a space-time of 26 dimensions which then, by introducing the supersymmetry, the number reduced to 10. "String theory is best understood in situations where we have a symmetry called `supersymmetry' which posits that particles come in pairs: for every boson, there is a fermion," Vafa says.

In the mid-1980s, there were five string theories, all in 10 dimensions, all supersymmetric, and all including gravitation. Then in the mid-1990s, a number of physicists, in particular Edward Witten, one of the greatest names in the history of string theory who was Vafa's thesis supervisor in 1985 at Princeton University, introduced an 11-dimensional theory, called M-theory, encompassing all early string theories. However, M-theory was ill-defined and has not lived up to the expectations, prompting Vafa to develop new compactifications of string theory, such as F-theory (originally in 1996). However, F-theory was not to fix a problem of M-theory. By introducing F-theory, Vafa described a different corner of string landscape from M-theory that has proven to be rather important.

In string theory, different compatifications lead to different solutions; each describes a unique universe with a unique set of elementary particles and fundamental interactions. The collection of the possible solutions, which is called "landscape," is immensely huge. The number of solutions is commonly thought to be 10500 but could be insanely higher (10272000).

Some string theorists tried to tackle the problem by connecting the theory to our universe's known properties – elementary particles and fundamental interactions. However, in the past two decades, F-theory has allowed physicists to try a different approach. Vafa has shown "how topological and geometric properties of extra dimensions in string theory can translate to physical properties in observed dimensions." F-theory helped researchers to describe everything very geometrically. Now they can use algebraic techniques to tackle geometric problems—to analyze the various ways of compactifying extra dimensions in F-theory and to find solutions. The geometry 'language' is the key feature of F-theory and turned it into a very powerful framework.

Vafa's contribution to the field is not limited to F-theory; he worked on formal aspects of the theory, including the discovery of duality symmetries and its elucidation. In the mid-1990s, Vafa and his colleague, Andy Strominger, showed that the entropy of black holes predicted by Bekenstein and Hawking can be derived from a deeper perspective in string theory as extended objects wrapped around extra dimensions of space. The result was considered the first clear demonstration of the principle of holography in a competing theory of quantum gravity. "This was one of the first non-trivial confirmations of string theory which showed the importance of both the extra dimensions as well as the extended nature of fundamental objects in string theory," he says.

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Vafa has initiated the Swampland program in recent years, showing how quantum gravitational consistency puts severe restrictions on consistent quantum theories. The term "swampland," which he coined in 2005, refers to those physical theories that are not compatible with string theory. He proposed swampland as a way for physicists to wade into the immense landscape of solutions and rule some large acreage of the landscape as physically inconsistent.

Vafa believes despite the immensity of the landscape of solutions, there is a unique solution that matches our universe. "I bet there is exactly one, but to pinpoint this is not going to be easy," he says.

String theory has often been criticized for just providing abstract mathematical results and making no measurable predictions. Vafa admits that the magnitude of technological difficulty to overcome in connecting string theory to experiments is currently beyond resolution, but "this should not be viewed as a weakness in the development of string theory," he says. "The theoretical progress we have made in string theory is one of the most remarkable achievements in the history of science," he believes. "Of course, we still need to understand more deeply what string theory is, and this will require many more decades to develop. When the dust settles, we would likely end up revolutionizing many branches of physics and mathematics.