Prof. Cumrun Vafa

The 2021 Mustafa Prize Laureate

**Designation: **Hollis Professor of Mathematics and Natural** **Philosophy, Harvard University

**Born: **1960

**Nationality: **Iran

**Work:**** **F-theory

**Field of the Prize: **Theoretical Physics

**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 10^{500} but could be insanely higher (10^{272000}).

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.

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