Effective action of β-deformed image SYM theory: Farewell to two-loop BPS diagrams Original Research Article

Within the background field approach, all two-loop sunset vacuum diagrams, which occur in the Coulomb branch of image superconformal theories (including image SYM), obey the BPS condition image, where the masses are generated by the scalars belonging to a background image vector multiplet. These diagrams can be evaluated exactly, and prove to be homogeneous quadratic functions of the one-loop tadpoles image, image and image, with the coefficients being rational functions of the squared masses. We demonstrate that, if one switches on the β-deformation of the image SYM theory, the BPS condition no longer holds, and then generic two-loop sunset vacuum diagrams with three non-vanishing masses prove to be characterized by the following property: image. In the literature, there exist several techniques to compute such diagrams. For the β-deformed image SYM theory, we carry out explicit two-loop calculations of the Kähler potential and image term. Our considerations are restricted to the case of β real.