Another example: -deformation

Let us deform the AdS action (1) in the following way:

   (2)

where are the currents of the global symmetry , and is a constant antisymmetric tensor.

This is the beta-deforation studied in our paper with Oscar Bedoya, Leandro Bevilaqua and Victor Rivelles.

It turns out that when is of the form for some constant , the deformation can be undone by a field redefinition. Therefore the space of linearized -deformations is:

   (3)