Duality is the incredible “two-in-one” combo of physics. Whenever two aspects of nature – electricity and magnetism, particles and waves, the field theory of particles and the theory of gravity – can be mathematically connected, new and unified theories of nature can emerge. But research collaborations can be powerful dualities in themselves.
That’s the case for the research duo of Dr. Kevin Costello, an University of Waterloo mathematical physicist who is also the Krembil William Rowan Hamilton Chair at Perimeter, and Dr. Natalie Paquette, a mathematical physicist at the University of Washington in Seattle and regular Visiting Fellow at Perimeter.
The mathematical physics duo is now putting a theory they have worked on in past years, known as twisted holography, together with a promising newer theory known as celestial holography. They hope a beautiful marriage of these two remarkable ideas will be a step forward in the decades-long quest for a unified theory of quantum gravity.
Their paper, “Celestial holography meets twisted holography: 4d amplitudes from chiral correlators,” was published in October in the Journal of High Energy Physics.
Both twisted holography and celestial holography are evolutions of the holographic duality, a remarkable concept and possible path to uniting the two great pillars of modern physics: Albert Einstein’s general relativity, our best description of gravity and spacetime, and quantum field theory, our best description of particles and the forces between them.
Unfortunately, these two theories simply don’t speak the same language. It is not easy to unite them, given that one theory is about a continuous, smooth spacetime and the other about discrete packets of energy.
The holographic duality has made the bridge-work easier by positing a hologram-like relationship connecting gravity in a negatively curved spacetime region called anti-de Sitter space to a conformal field theory, which describes particles on that region’s boundary.
Modern-day measurements lead cosmologists to conclude that the universe is approximately flat (possibly with a tiny amount of positive curvature). Unlike the curved soup can or bottle universe, a “flat” spacetime means Euclidean spatial geometry, where parallel lines always run parallel and never meet. Ideally, scientists would like a model that is closer to the flatish spacetime we live in.
Celestial holography might get them there. In celestial holography, the boundary of the universe’s celestial sphere is infinitely far away, so the spacetime region inside it would look essentially flat.
The supersymmetric equations are what make all this work. These equations can be used on this “geometric playground” to arrive at something “much more physical and applicable to the real world,” Paquette says.
“You can actually get pretty close to the spacetime you might be interested in studying,” Costello adds.
But the work with celestial holography that Costello and Paquette are doing is not just useful in the realm of understanding quantum gravity.
Their December paper is about the scattering of particles. In this work, the momentum of the particle is determined by a point on the celestial sphere, so it too is related to celestial holography.
“It’s nice when some math from seemingly out of left field comes in and provides a very beautiful and concise way of thinking about some computation,” says Paquette.
Ultimately, this work will deepen our understanding of nature, in the realm of the very small as well as that of the cosmos.
“It’s nice when some math from seemingly out of left field comes in and provides a very beautiful and concise way of thinking about some computation,” says Paquette.