Abstract
We calculate the one loop beta function for the would-be marginal coupling on the world sheet of the k deformed sigma models associated to a quantum group with q = e iπ/k. This includes the bosonic principal chiral models and symmetric space sigma models but also the k deformed semi-symmetric space sigma model describing strings in a deformation of AdS5 × S 5. The world sheet sigma model is a current-current deformation of the gauged WZW model for the supergroup PSU(2, 2|4) with level k. In the string theory context the beta function is shown to vanish because of the vanishing of the Killing form of PSU(2, 2|4) which is another piece of evidence that the k deformed theories define consistent string theories.
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Appadu, C., Hollowood, T.J. Beta function of k deformed AdS5 × S 5 string theory. J. High Energ. Phys. 2015, 95 (2015). https://doi.org/10.1007/JHEP11(2015)095
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DOI: https://doi.org/10.1007/JHEP11(2015)095