We carry out a detailed superspace analysis of the OPE of two N = 2 stresstensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of N = 2 SCFTs, imply an analytic bound on the central charge c. This bound is valid for any N = 2 SCFT regardless of its matter content and flavor symmetries, and is saturated by the simplest Argyres-Douglas fixed point. We also present a partial conformal block analysis for the scalar superconformal primary of the multiplet.

Assuming an effective gravitational action with scale dependent coupling constants, a consistency condition for the local form of the cut-off scale is derived. The approach is applied to homogeneous cosmology and running couplings with an ultraviolet fixed point. Within the given approach this allows to derive bounds on the value of the fixed point.

Using superspace techniques, we compute the mixed OPE between an N = 2 stress-tensor multiplet, a chiral multiplet and a flavor current multiplet. We perform a detailed analysis of the three-point function between two of the mentioned multiplets and a third arbitrary operator. We then solve all the constraints coming from the N = 2 superconformal symmetry and from the equations of motion and/or conservation equations, and obtain all the possible operators that can appear in the expansion. This calculation is the first step towards a more general superconformal block analysis of mixed correlators in N = 2 theories.

In this work we propose a systematic way to compute the logarithmic divergences of composite operators in the pure spinor description of the AdS 5 × S 5 superstring. The computations of these divergences can be summarized in terms of a dilatation operator acting on the local operators. We check our results with some important composite operators of the formalism.