PhD. defense by Kasper Engel Vardinghus – University of Copenhagen

PhD. defense by Kasper Engel Vardinghus

Boundaries of Integrability in AdS/dCFT

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 discussed 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.