Abstract
We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal invariance of correlation functions, and imposes some relations between correlation functions of different orders. Numerical analysis shows that these conditions are incompatible unless the critical exponents take particular values, or more precisely that they must belong to a small island in the parameter space.
Highlights
Physics has many emergent laws, which follow in a non-obvious way from more fundamental microscopic laws
One example is the Gibbs distribution of equilibrium statistical mechanics: the probability for the system in thermal equilibrium at temperature T to be found in a state n of energy En is proportional to exp(−En/T )
We will describe the axioms of Conformal Field Theory (CFT) on Rd, d 3
Summary
Physics has many emergent laws, which follow in a non-obvious way from more fundamental microscopic laws Whenever this happens, we have two separate goals: to understand how the emergent law arises, and to explore its consequences. One may be interested in deriving this emergent law from microscopic models of thermalization, or in exploring the myriad of its physical consequences. This text, based on a recent talk for an audience of mathematical physicists, is about the “conformal field theory” (CFT), a set of emergent laws governing critical phenomena in equilibrium statistical mechanics (such as the liquid–vapor critical point or the Curie point of ferromagnets). An excellent set of recorded lectures is [5]
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