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In this paper, new bounds on possible variations of the fine structureconstant, $\alpha$, for a class of runaway dilaton models are performed. Byconsidering a possible evolution with redshift, $z$, such as$\frac{\Delta\alpha}{\alpha}=-\gamma\ln(1+z)$, where in $\gamma$ are thephysical properties of the model, we constrain this parameter by using adeformed cosmic distance duality relation jointly with gas mass fraction (GMF)measurements of galaxy clusters and luminosity distances of type Ia supernovae.The GMF's used in our analyses are from cluster mass data from 82 galaxyclusters in the redshift range $0.12<z<1.36$, detected via theSunyaev-Zeldovich effect at 148 GHz by the Atacama Cosmology Telescope. Thetype Ia supernovae are from the Union2.1 compilation. We also explore thedependence of the results from four models used to describe the galaxyclusters. As a result no evidence of variation was obtained.

Limits on evolution of the fine-structure constant in runaway dilaton models from Sunyaev-Zeldovich Observations