Physicists at the Indian Institute of Science (IISc) have discovered that pure mathematical formulae developed by Srinivasa Ramanujan over a century ago for calculating the value of pi are fundamentally connected to modern high-energy physics. The study demonstrates that Ramanujan's work mirrors the theoretical models describing phenomena such as turbulence, percolation, and aspects of black holes.
The Link to Conformal Field Theories
In 1914, Srinivasa Ramanujan published 17 highly efficient mathematical formulae for calculating pi. These foundational formulae remain crucial today, forming the basis for advanced computational algorithms—including the Chudnovsky algorithm used by supercomputers to calculate pi to trillions of digits.
Researchers Aninda Sinha, Professor at the Centre for High Energy Physics (CHEP) at IISc, and Faizan Bhat, a former IISc PhD student, sought a physics-based explanation for the existence of these equations. Their investigation revealed that Ramanujan’s formulae naturally arise within a broad class of models known as conformal field theories (CFTs), specifically logarithmic conformal field theories.
Conformal field theories describe physical systems exhibiting scale invariance symmetry, meaning the system appears identical regardless of how much one zooms in, a characteristic seen in structures like fractals or water at its critical point (where liquid and vapour are indistinguishable).
Significance for Fundamental Physics
The more specific logarithmic conformal field theories are vital for explaining critical behaviour across diverse physical systems:
Percolation: The process of how things spread through a medium.
Turbulence: The onset of complex fluid flow.
Black Holes: Certain theoretical descriptions of these cosmic objects.
The researchers found that the mathematical structure underlying the starting points of Ramanujan's equations emerges naturally in the mathematics of these logarithmic CFTs. This discovery provides a new and efficient tool for calculating specific quantities within these physical theories, potentially accelerating the understanding of complex phenomena like turbulence and percolation.
According to the researchers, this connection suggests that Ramanujan, working purely in mathematics in the early 20th century, inadvertently anticipated structures now central to understanding the universe.
Editor’s Note: Based on a press release from IISc.
