A New Kind of Symmetry Shakes Up Physics

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It’s not an exaggeration to say that every major advance in physics for more than a century has turned on revelations about symmetry. It’s there at the dawn of general relativity, in the birth of the Standard Model, in the hunt for the Higgs.

For that reason, research across physics is now building to a crescendo. It was touched off by a 2014 paper, “Generalized Global Symmetries,” which demonstrated that the most important symmetries of 20th-century physics could be extended more broadly to apply in quantum field theory, the basic theoretical framework in which physicists work today.

This reformulation, which crystallized earlier work in the area, revealed that disparate observations physicists had made in the past 40 years were really manifestations of the same lurking symmetry. In doing so, it created an organizing principle that physicists could use to categorize and understand phenomena. “That’s really a stroke of genius,” said Nathaniel Craig, a physicist at the University of California, Santa Barbara.

The principle identified in the paper came to be known as “higher symmetries.” The name reflects the way the symmetries apply to higher-dimensional objects such as lines, rather than lower-dimensional objects such as particles at single points in space. By giving the symmetry a name and language and by identifying places it had been observed before, the paper prompted physicists to search for other places it might appear.

Physicists and mathematicians are collaborating to work out the mathematics of these new symmetries — and in some cases they’re discovering that the symmetries work like a one-way street, a notable contrast to all other symmetries in physics. At the same time, physicists are applying the symmetries to explain a wide range of questions, from the decay rate of certain particles to novel phase transitions like the fractional quantum Hall effect.

“By putting a different perspective on a known sort of physical problem, it just opened up a huge new area,” said Sakura Schafer-Nameki, a physicist at the University of Oxford.

The symmetries of 20th-century physics were built on points. Higher symmetries are based on one-dimensional lines.

Symmetry Matters

To understand why a paper that merely points out the breadth of lurking symmetries can make such a big impact, it helps to first understand how symmetry makes life easier for physicists. Symmetry means fewer details to keep track of. That’s true whether you’re doing high-energy physics or laying bathroom tile.

The symmetries of a bathroom tile are spatial symmetries — each can be rotated, flipped upside down or moved to a new spot. Spatial symmetries play an important simplifying role in physics too. They’re prominent in Einstein’s theory of space-time — and the fact that they pertain to our universe means physicists have one less thing to worry about.

“If you’re doing an experiment in a lab and you rotate it, that shouldn’t change your answer,” said Nathan Seiberg, a theoretical physicist at the Institute for Advanced Study in Princeton, New Jersey.

Nathan Seiberg was a co-author on the 2014 paper that developed the notion of higher symmetries.

Andrea Kane/Institute for Advanced Study

The symmetries that are most important in physics today are subtler than spatial symmetries, but they carry the same meaning: They’re constraints on the ways that you can transform something to ensure that it’s still the same.

In an epochal insight in 1915, the mathematician Emmy Noether formalized the relationship between symmetries and conservation laws. For example, symmetries in time — it doesn’t matter if you run your experiment today or tomorrow — mathematically imply the law of conservation of energy. Rotational symmetries lead to the law of conservation of angular momentum.

“Every conservation law is associated with a symmetry, and every symmetry is associated with a conservation law,” Seiberg said. “It’s well understood and it’s very deep.”

This is just one of the ways that symmetries help physicists understand the universe.

Physicists would like to create a taxonomy of physical systems, classifying like with like, in order to know when insights from one can be applied to another. Symmetries are a good organizing principle: All systems exhibiting the same symmetry go in the same bucket.

Furthermore, if physicists know a system possesses a given symmetry, they can avoid a lot of the mathematical work of describing how it behaves. The symmetries constrain the possible states of the system, which means they limit the potential answers to the complicated equations that characterize the system.

“Typically, some random physical equations are unsolvable, but if you have enough symmetry, then the symmetry constrains the possible answers. You can say the solution must be this because it’s the only symmetric thing,” said Theo Johnson-Freyd of the Perimeter Institute for Theoretical Physics in Waterloo, Canada.

Symmetries convey elegance, and their presence can be obvious in hindsight. But until physicists identify their influence, related phenomena can remain distinct. Which is what happened with a host of observations physicists made starting in the early 1970s.

Fields and Strings

The conservation laws and symmetries of 20th-century physics take pointlike particles as their primary objects. But in modern quantum field theories, quantum fields are the most basic objects, and particles are just fluctuations in these fields. And within these theories it’s often necessary to go beyond points and particles to think about one-dimensional lines, or strings (which are conceptually distinct from the strings in string theory).

In 1973, physicists described an experiment that involved placing a superconducting material between poles of a magnet. They observed that as they increased the strength of the magnetic field, particles arranged themselves along one-dimensional superconducting threads running between the magnetic poles.

The next year Kenneth Wilson identified strings — Wilson lines — in the setting of classical electromagnetism. Strings also appear in the way the strong force acts among quarks, which are the elementary particles that make up a proton. Separate a quark from its antiquark, and a string forms between them that pulls them back together.

The point is that strings play an important role in many areas of physics. At the same time, they’re mismatched to traditional conservation laws and symmetries, which are expressed in terms of particles.

“The modern thing is to say we’re not only interested in the properties of points; we’re interested in the properties of lines or strings, and there can also be conservation laws for them,” said Seiberg, who co-wrote the 2014 paper along with Davide Gaiotto of the Perimeter Institute, Anton Kapustin of the California Institute of Technology, and Brian Willett, who was at the time a postdoc at the Institute for Advanced Study.

The paper presented a way of measuring charge along a string and establishing that charge remains conserved as the system evolves, just as total charge is always conserved for particles. And the team did it by shifting their attention from the string itself.

Read the full article over at Quanta Magazine


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