Beta Function of k Deformed AdS_5 x S^5 String Theory

Understand

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=exp(i pi/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 AdS_5 x 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.