Prof. Jun Nishimura of KEK Theory Center and his collaborators performed numerical simulations of superstring theory, which is a fundamental theory that describes our universe, and showed that the equivalence between the imaginary-time theory and the real-time theory, which has been widely believed among researchers, does not hold true in this case. The research results were published in Physical Review Letters on May 27, 2025 (US Eastern Time). 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.211601

The imaginary-time theory is constructed by replacing real-valued time with a pure imaginary number (a fictitious number that becomes negative real number when squared). By doing so, time coordinates can be treated on an equal footing with spatial coordinates as one can show by Einsteinʹs theory of relativity. This technique is not only the basis of various studies in particle physics, but is also well known for being used by Dr. Hawking and others to describe quantum tunneling phenomenon that is believed to have occurred when the universe was created from nothing. For these reasons, the imaginary-time theory has often been used when studying questions such as whether a (3+1)-dimensional expanding universe emerges from superstring theory in (9+1)-dimensional space-time, which is considered to be the ultimate theory describing the universe. However, the present calculation made it clear that the equivalence of the imaginary-time theory and the real-time theory does not generally hold, at least in theories that include the quantum effects of space-time itself, such as superstring theory. It is expected that further developments in numerical simulations of real-time theories will shed light on various problems, such as the beginning of the universe. This research is based on collaboration with Chien-Yu Chou and Ashutosh Tripathi, students majoring in particle and nuclear physics at SOKENDAI.