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In physics, the beta-function measures the dependence of the strength of an interaction upon the energy. According to the theory of renormalization group, the coupling constants, such as the fine-structure constant, in quantum field theory are not really constant, but they depend on the energy scale (in the usual case of gauge theory in four spacetime dimensions, the dependence is logarithmic). The beta-function exactly measures this dependence:

For most interactions, the beta-function is positive, and therefore the force grows stronger at very short distances (higher energies); this usually results in the Landau pole. However, Yang-Mills theory (e.g. quantum chromodynamics) can lead to a negative beta-function - which is known as asymptotic freedom.