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2d non-linear sigma models are widely used in high and low energy physics.
In my talk I will present how to compute the one-loop anomalous dimension for fields
in some cases in which the background is a coset space. I will review the formula for the case in which the background is a symmetric coset (that admit a $Z_2$ automorphism) and present the new result for $Z_4$-cosets. The last result is applicable to the string described by the hybrid model formalism on $AdS_5\times S^5$ and it is relevant for AdS/CFT.