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In the paper of Intriligator, Seiberg, and Shih from 2007, they give an expression for the effective potential on the pseudo-moduli space $X$, estimated at large $X$ (equation 1.3).

In this equation, "$\gamma$ is the anomalous dimension of a particular linear combination of them". Later on in the paper they give examples for this (eq. 4.9).

What is the formula for this $\gamma$ and how do we reach this expression?

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I suspect the derivation of the formula for the potential is in Witten's paper cited as 18, inspirehep.net/record/167850 - The "formula" for the anomalous dimension is whatever it always is. It appears in the exponent for the 2-point function of this operator, and the anomalous (non-classical) contribution itself may be determined from the coefficient of a log divergence in this 2-point function. –  LuboŇ° Motl Dec 24 '12 at 11:41

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