Anomalies in Superconformal Field Theories

This thesis presents work related to anomalies in superconformal field theories (SCFTs). Recent holographic computations proved the existence of new supersymmetry anomalies in N = 1 SCFTs with an anomalous R-symmetry. This was also confirmed in the context of the Wess-Zumino (WZ) consistency conditions. Motivated by these results, we provide a comprehensive analysis of the free and massless WZ model in perturbation theory. The WZ model is classically invariant under the superconformal group SU(2, 2|1), but some of these symmetries are broken by quantum anomalies. There are well known bosonic anomalies associated with R-symmetry and scale invariance, as well as fermionic anomalies associated with the gamma trace of the supercurrent (usually known as S-supersymmetry). We provide the first rigorous loop computation which shows that Q-supersymmetry of conformal supergravity is anomalous at the level of the 4-point correlators, confirming the holographic and WZ consistency conditions computations. In particular, we focus on the Ward identities of the 4-point correlator of two supercurrents and two R-currents <QQJ J ¯ >. The results are verified by two different regulators, namely the cut-off and the Pauli-Villars regularization procedures. We also obtain all the standard anomalies of the WZ model that is coupled to conformal supergravity. Our results also show that the form of the anomalies and the part of the symmetry they break depend on the multiplet of conserved currents one uses. In particular, the conformal multiplet in the renormalized theory is necessarily anomalous in Q- and S-supersymmetries, while in the Ferrara-Zumino (FZ) multiplet –the minimal massive multiplet– there exists a manifestly non anomalous combination of Q- and S- supersymmetries of the conformal multiplet. We give the counterterm that relates the two multiplets in the correlation functions of interest. Finally, in the context of the loop computation, we shed light on many subtle issues on the regulators and the derivation of the Ward identitie