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

TL;DR

This paper computes the one-loop beta function for k deformed sigma models related to AdS_5 x S^5, showing that the models are consistent string theories due to the vanishing beta function.

Contribution

It provides the first calculation of the one-loop beta function for k deformed AdS_5 x S^5 string models, confirming their consistency.

Findings

Beta function vanishes for the k deformed models.

Supports the consistency of the deformed string theories.

Includes analysis of bosonic and semi-symmetric space sigma models.

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=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.