Abstract: |
The idea of building up macroscopic phenomena from microscopic constituents is as old as science itself, and has been a perennial theme in theoretical physics since the dawn of the 20th century. Recently, many groups have begun to study this point of view in the context of conformal field theory, systematically applying the notions of Bohr's correspondence principle to understand the transition from the microscopic realm to the macroscopic regime, within the framework of the axioms of CFT. In this colloquium I will recount some of the ancient and modern history of this set of ideas, before turning to their modern incarnation as the "Large Quantum Number Expansion" of observables in quantum physics. I will discuss the application of the expansion to theories both old -- such as the Wilson-Fisher O(2) model, describing the transition to superfluidity in liquid helium -- and new -- such as strongly interacting gauge theories with extended superconformal symmetry. I will highlight the phenomenal accuracy of the expansion, generating predictions confirmed with an accuracy of .01%-.1% for quantum numbers of order 1, to 1 part in 10 to the 17 for quantum numbers of order 100. |