Master Defence: Aleix Gimenez Grau and Matthias Volk

Title: One-Loop One-Point Functions in Non-Supersymmetric AdS/dCFT

Abstract: We study the defect version of N = 4 supersymmetric Yang-Mills theory dual to the D3-D7 probe-brane system with D7 brane geometries AdS4 × S2 × S2 and AdS4 × S4 stabilized by background fluxes. On the field-theory side, these geometries correspond to classical solutions for the scalars with SO(3) × SO(3) and SO(5) symmetry respectively. The classical solutions lead to non-diagonal quadratic terms in the action mixing both flavor and color degrees of freedom. We solve the mixing problem, i.e. obtain the spectrum and mass eigenstates of the theory, using a modifications of the techniques that were previously used to find the spectrum in the related D3-D5 probe-brane system. For the solution with SO(3) × SO(3) symmetry we identify the propagators between the fields in the action enabling us to perform perturbative calculations in terms of Feynman diagrams. We first calculate the planar one-loop correction to the vacuum expectation values of the scalars in dimensional reduction and find that it is UV-finite and non-vanishing. We then proceed to find the one-loop correction to the one-point function of the BMN vacuum operator in the planar limit. The one-point function can also be calculated in a supergravity approximation of the dual string theory and we find that the results of both theories agree exactly in a certain double-scaling limit. The setup breaks supersymmetry completely as well as conformal symmetry partially and the match between the two sides therefore constitutes a very non-trivial check of the AdS/CFT correspondence.