Thesis:

On CFTs and conformal techniques in AdS

Conformal symmetry is a fundamental tool in the study of string theory, critical phenomena, and interacting quantum field theories. This doctoral thesis focuses on conformal methods applied to two main areas: Type IIB superstring theory in an AdS5 x S5 background, and four-dimensional N = 2 supersymmetric field theories. In the case of N = 2 theories, we take an initial step toward computing superconformal blocks for mixed operators. For chiral and real half-BPS operators, these blocks can be constructed using chiral or harmonic superspace techniques. However, no general method exists for more complex multiplets. This work presents a procedure to compute operator product expansions (OPE) involving an N = 2 stress-tensor multiplet, a chiral multiplet, and a flavor current multiplet using superspace techniques. A general bound for the central charge of interacting theories is also derived. On the string theory side, a systematic method is proposed to compute logarithmic divergences of composite operators in the pure spinor formalism of the AdS5 x S5 superstring. These divergences are described in terms of a dilatation operator acting on local operators. The results are verified using key composite operators in the formalism. Finally, the pure spinor AdS string is constructed using supertwistor techniques.