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 twopoint functions in probe brane field theories
The topic of this thesis is the computation of one and twopoint correlation functions in defect conformal field theories (dCFTs) that are holographically dual to certain probe brane configurations. The defect field theories discussed are all domain walls of N=4 super YangMills theory that interface between a U(N−k) gauge group and a U(N) gauge group. dCFTs may have nontrivial onepoint functions, and for the SO(3)×SO(3) symmetric probe D7 defect we compute onepoint functions at treelevel using integrability of the N=4 spectrum. The onepoint 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 onepoint 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 YangBaxter equation that reduces to the SO(6)sector matrix product state at zero rapidity.
In dCFTs twopoint functions between operators of different conformal dimensions may be nontrivial and in particular we consider the computation of twopoint functions in the probe D5 defect for simple operators. In dCFTs the twopoint functions can be expanded in conformal blocks providing a relation between the one, two and threepoint functions.
