ON CFT AND CONFORMAL TECHNIQUES IN AdS

Abstract

Conformal symmetry is an essential tool for the study of string theory, critical phenomenaand interacting quantum eld theories, among other examples. In this thesis, we focuson conformal techniques for two theories: Type IIB superstring theory on an AdS5 S5background, and N = 2 theories in four dimensions.On the N = 2 theory, we will give a rst step towards the computation of superconformalblocks for mixed operators. For chiral and real half-BPS operators, their superconformalblock expansion can be achieved using chiral or harmonics superspace techniques, respectively.For more general multiplets, no general tool is available. A rst step towards this goalis to obtain the OPE for those general multiplets. In this thesis we show how to computemixed OPEs between an N = 2 stress-tensor multiplet, a chiral multiplet and a avor currentmultiplet using superspace techniques. A general bound for the central charge of interactingtheories will be obtained using the N = 2 stress-tensor multiplet OPE.On the string theory side, we propose a systematic way to compute the logarithmicdivergences of composite operators in the pure spinor description of the AdS5 S5 superstring.The computations of these divergences can be summarized in terms of a dilatation operatoracting on the local operators. We check our results with some important composite operatorsof the formalism. Finally, we construct the pure spinor AdS string using supertwistors.