NYC Gazette

String theory, a framework developed over five decades ago to explain the formation of matter, has yet to be proven. However, physicists have made progress in validating it using a new mathematical method that suggests its "inevitability."

String theory proposes that the fundamental components of nature are one-dimensional vibrating strings. These strings move at different frequencies, determining the type of particle they form, similar to how string instruments produce various musical notes.

In research published in Physical Review Letters, scientists from New York University and Caltech explored the question: “What is the math question to which string theory is the only answer?” This method, known as the “bootstrap,” refers to producing results without external assistance or input.

The bootstrap approach has helped physicists understand why general relativity and certain particle theories are mathematically inevitable under specific criteria. However, this question had not been answered for string theory until now.

The researchers found a way to bootstrap string amplitudes by creating mathematical formulas. By applying special conditions on their formulas for scattering amplitudes—which describe particle interactions—the team discovered that string theory's amplitudes were the only consistent solution.

A visualization shows allowed values of "dial settings" in scattering amplitudes describing interaction probabilities in models introduced by this work. Green regions align with unitarity, conserving quantum mechanical probability. These models result from new mathematical methods producing deformations of string theory. Image credit goes to Grant Remmen from NYU's Department of Physics.

“This paper provides an answer to this string-theory question for the first time,” says Grant Remmen, a James Arthur Postdoctoral Fellow at NYU’s Center for Cosmology and Particle Physics and co-author of the paper. “Now that these mathematical conditions are known, it brings us a step closer to understanding if and why string theory must describe our universe.”

Other authors include Clifford Cheung, a theoretical physics professor at Caltech, and Aaron Hillman, a Caltech postdoctoral researcher. They suggest this breakthrough may help better understand quantum gravity—a field aiming to reconcile Einstein’s relativity with quantum mechanics.

“This approach opens a new area of study in analyzing the uniqueness of string amplitudes,” explains Remmen. “The development of tools outlined in our research can be used to investigate deformations of string theory, allowing us to map a space of possibilities for quantum gravity.”

This study was funded by a grant from the US Department of Energy (DESC0011632).