Young physicist wins prize for contribution to quantum field theory

Sackler prize awarded by Tel Aviv University is third important international award won by Pedro Vieira, who works at Canada’s Perimeter Institute and at ICTP-SAIFR in Brazil.

By José Tadeu Arantes  |  Agência FAPESP – The young Portuguese physicist Pedro Vieira is one of the winners of the 2018 Sackler Prize in Physics. Every year, up to two Raymond and Beverly Sackler International Prizes, each worth 100,000 US dollars, are awarded at Tel Aviv University (TAU) to researchers aged not more than 40. The 2018 prizes were awarded for novel contributions to quantum field theory. Vieira will receive his award in March, together with Zohar Komargodski from Israel’s Weizmann Institute.

This will not be the first important international award won by Vieira. In 2015, his work was recognized by the European Physical Society, which awarded him its Gribov Medal, and by a Sloan Research Fellowship from the Alfred P. Sloan Foundation.

Vieira divides his working year between the Perimeter Institute for Theoretical Physics in Waterloo, Canada, and the South American Institute for Fundamental Research (ICTP-SAIFR) in São Paulo, Brazil. Hosted by the São Paulo State University’s Theoretical Physics Institute (IFT-UNESP), ICTP-SAIFR is a collaboration between UNESP and the International Center for Theoretical Physics (ICTP), based in Trieste, Italy, and has funding from FAPESP.

While still a student in Portugal, Vieira founded the Mathematica Summer School on Theoretical Physics, which continues to meet annually on an itinerant basis, with the aim of helping physicists learn to use Mathematica software while providing a discussion forum on advanced topics in theoretical physics.

Vieira gave an interview to Agência FAPESP from Porto, in Portugal, during his vacations. Highlights follow.

Agência FAPESP – As well as important contributions to the development of quantum field theory (QFT) and string theory, you’re also known for your ability to talk about the most complicated topics in physics simply, intuitively and accessibly for those who haven’t mastered the necessary mathematical language. So please give us a simple description of your research interests.
Pedro Vieira – I do indeed study QFT, a combination of two disciplines: quantum physics, which describes everything that’s very small; and relativity, which describes everything that’s very fast. When you have something that’s both very small and very fast, such as the fundamental particles of matter, you need to combine quantum physics and relativity. 

Agência FAPESP – That has been a major challenge for physicists ever since Einstein.
Pedro Vieira – Yes, because what happens is that the resulting field theory can be easy or hard. It’s easy when the particles we’re studying don’t interact a lot with each other, as in the case of light, for example. The photons that make up a ray of light move freely alongside each other, practically without interacting. If we understand what happens to one, we understand what happens to all of them. But field theory gets hard when the particles interact strongly with each other. In this case, the situation is so complex that we lack the mathematics to describe what happens. My work focuses on developing that mathematics.

Agência FAPESP – How do you proceed?
Pedro Vieira – I develop physical intuition on one hand and mathematical language on the other. Both are required to describe an actual situation – both physical images and mathematical techniques. Within all that, I also study so-called string theory. In string theory, the idea is that particles aren’t small spheres or dots, as conceived by classical and even contemporary physics, but small strings or elastic bands. Seen from afar, these entities look like dots, but when seen up close, they prove to be strings, elastic bands. One hypothesis, which physicists consider highly attractive, very elegant, is that maybe all particles – quarks, electrons, neutrinos, photons, etc. – are actually strings. 

Agência FAPESP – The same strings?
Pedro Vieira – The same strings, with different modes of vibration. The waves propagate along the strings just as they do when you pluck a guitar string.

Agência FAPESP – The theory admits the existence of open and closed strings, does it not?
Pedro Vieira – An open string is like a segment or any line with two endpoints. As it moves through spacetime, an open string describes a surface similar to that of a rectangle, which may be smooth or wavy. A closed string is like a circle or any curved line that reconnects with itself to form a closed loop. As it moves through spacetime, a closed string describes a tube, which may be a regular tube like the side of a cylinder, or an irregular tube with corrugations, twists and knots. So studying string theory is studying these rectangles and tubes in spacetime, the rectangles and tubes described by strings as they move.

Agência FAPESP – And in this context, how do you conceive of the phenomena called interactions between particles in the standard model?
Pedro Vieira – This is where it gets complicated. The strings start to divide or join up with other strings. So the rectangles and tubes also divide or join up. The mathematical description of all these surfaces becomes highly complex. I had an intuition that enabled me to think up a trick to work around the mathematical difficulty. In the case of a tube, you cut off a piece in the shape of a hexagon. This creates a basic element that’s easy to study using the mathematic tools we have now. If you put several of these hexagons side by side, you can obtain something like a tiled surface and that way you can describe any tube. I understood that tubes, the movements of closed strings, can be described using hexagons, and that rectangles, the movements of open strings, can be described using pentagons. It seems to me that all kinds of moving strings can be described using hexagons and pentagons. 

Agência FAPESP – What else can you say about this?
Pedro Vieira – When we think about strings moving through spacetime, we realize they can move in many directions. They move in four-dimensional spacetime (three for space and one for time), but the surface of the tubes formed by the movement of closed strings has only two dimensions. The fact that it’s a two-dimensional surface is very important because it tells us that if we can build a clearer picture of the geometry of this two-dimensional surface, we’ll be able to understand the geometry of the tubes that are in more-dimensional space. It’s far easier to study two-dimensional space than any space with more than two dimensions. If we focus only on the tube’s two-dimensional surface, what happens if a wave moves along this surface, like a wave on the surface of the sea? This wave can only go up or down, right or left. Only these possibilities exist. When two or three waves move on this surface, they collide. So studying physics in two dimensions is studying these waves that travel along lines and cross each other. This physics can often be studied using a technique known as “integrability”. This technique lets us study these waves and what happens to them when they cross each other. Integrability was used in some technological applications of the physics of condensed matter, to study materials that are practically one-dimensional. Not strictly one-dimensional, of course, but almost. So this technique can be used to study everything that happens when particles can move only in one dimension.

Agência FAPESP – How has integrability been applied to string theory?
Pedro Vieira – This was a big surprise, which happened in 2003, when it was realized that strings themselves were one-dimensional objects, and so we could use integrability, this same simplification, to study string theory. It seems obvious now, but no one had realized that before. What we’ve understood recently is that with this mathematic technique, integrability, we can consider a fragment of the tube’s surface in the shape of a hexagon and imagine waves moving on it. A wave starts from one of the six sides of the hexagon and travels across to the other side. Another wave starts from a different side, and so on. Sometimes these waves meet and have to cross over or under each other. I understood how to study these hexagons even when they’re violently agitated, with many waves traveling in different directions. The technique of integrability makes it possible to study them. Because any surface can be divided into hexagons, by studying the hexagon, we can describe any surface, which in turn describes processes that occur in four-dimensional spacetime. This is one of the tricks I’ve developed in recent years – the trick of using two-dimensional physics to study many-dimensional physics.