String theory, conceptualized more than 50 years ago as a framework to explain the formation of matter, remains elusive as a "provable" phenomenon. But a team of physicists has now taken a significant step forward in validating string theory by using an innovative mathematical method that points to its "inevitability."
String theory posits that the most basic building blocks of nature are not particles, but, rather, one-dimensional vibrating strings that move at different frequencies in determining the type of particle that emerges -- akin to how vibrations of string instruments produce an array of musical notes.
In their work, reported in the journal Physical Review Letters, New York University and Caltech researchers posed the following question: "What is the math question to which string theory is the only answer?" This approach to understanding physics is known as the "bootstrap," which is reminiscent of the adage about "pulling yourself up by your bootstraps" -- producing results without additional assistance or, in this case, input.
The bootstrap has previously allowed physicists to understand why general relativity and various particle theories -- like the interactions of gluons inside of protons -- are mathematically inevitable: they are the only consistent mathematical structures, under certain criteria.
However, the same question had not previously been answered for string theory: What criteria uniquely determine it by mathematically picking it out from the set of all possible theories?
In the Physical Review Letters paper, the scientists discovered a way to bootstrap these string amplitudes -- specifically, constructing them through the creation of mathematical formulas. By implementing special mathematical conditions on their formulas for scattering amplitudes -- which describe how particles interact and ultimately form -- the group found that the amplitudes of string theory emerged as the only consistent answer.
"This paper provides an answer to this string-theory question for the first time," says Grant Remmen, a James Arthur Postdoctoral Fellow in NYU's Center for Cosmology and Particle Physics and one of the authors 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."
The paper's authors, who also included Clifford Cheung, a professor of theoretical physics at Caltech, and Aaron Hillman, a Caltech postdoctoral researcher, add that this breakthrough may be useful in better understanding quantum gravity -- it seeks to reconcile Einstein's theory of relativity, which explains large-scale gravity, with quantum mechanics, which describes particle activity at the smallest scales.
"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 research was supported by a grant from the US Department of Energy (DESC0011632).