In string theory, S-duality relates a system with one value of this quantity to a system where this quantity is a reciprocal of that value. When calculating amplitudes from Feynman diagrams, the vertex factor is equal, up to sign and a product of i, to the total of this quantity for that vertex. One instance of this quantity is the square of the ratio of the electron mass to the Planck mass, and the lifetime of the muon is inversely proportional to the square of one of these quantities named for Fermi. The derivative of this quantity with respect to the natural log of the energy scale gives the factor beta, which is zero for scale-invariant theories and encodes the (*) "running" of this quantity. This quantity in QCD decreases logarithmically with increasing energy, a fact known as asymptotic freedom, while in another theory it blows up at the Landau pole. For the electromagnetic interaction in QED, a dimensionless version of this quantity is equal to approximately 1 over one-hundred thirty-seven and is called the fine-structure constant. For 10 points, give 
In string theory, S-duality relates a system with one value of this quantity to a system where this quantity is a reciprocal of that value. When calculating amplitudes from Feynman diagrams, the vertex factor is equal, up to sign and a product of i, to the total of this quantity for that vertex. One instance of this quantity is the square of the ratio of the electron mass to the Planck mass, and the lifetime of the muon is inversely proportional to the square of one of these quantities named for Fermi. The derivative of this quantity with respect to the natural log of the energy scale gives the factor beta, which is zero for scale-invariant theories and encodes the (*) "running" of this quantity. This quantity in QCD decreases logarithmically with increasing energy, a fact known as asymptotic freedom, while in another theory it blows up at the Landau pole. For the electromagnetic interaction in QED, a dimensionless version of this quantity is equal to approximately 1 over one-hundred thirty-seven and is called the fine-structure constant. For 10 points, give this constant that, for a given theory, characterizes the strength of the interaction.
In string theory, S-duality relates a system with one value of this quantity to a system where this quantity is a reciprocal of that value.
coupling constant