Kasper Engel Vardinghus

A thesis for the degree of Doctor of Philosophy defended March 2019.

The PhD School of Science, Faculty of Science, Theoretical Particle Physics and Cosmology, Niels Bohr Institute, University of Copenhagen

Supervisors:
Prof. Charlotte Kristjansen

Boundaries of Integrability in AdS/dCFT

One- and two-point functions in probe brane field theories

The topic of this thesis is the computation of one- and two-point correlation functions in defect conformal field theories (dCFTs) that are holographically dual to certain probe brane configurations. The defect field theories dis-cussed are all domain walls of N=4 super Yang-Mills theory that interface between a U(N−k) gauge group and a U(N) gauge group. dCFTs may have non-trivial one-point functions, and for the SO(3)×SO(3) symmetric probe D7 defect we compute one-point functions at tree-level using integrability of the N=4 spectrum. The one-point functions are computed for SU(2)-sector operators with a small number of excitations and a general form for large operators is conjectured.The explicit expressions for the one-point functions shows that the matrix product state for the SO(3) SO(3) symmetric probe D7 defect is not an integrable spin chain state. In a related setup, the probe D5 defect, we present a new solution of the boundary Yang-Baxter equation that reduces to the SO(6)-sector matrix product state at zero rapidity.

In dCFTs two-point functions between operators of different conformal dimensions may be non-trivial and in particular we consider the computation of two-point functions in the probe D5 defect for simple operators. In dCFTs the two-point functions can be expanded in conformal blocks providing a relation between the one-, two- and three-point functions.