PhD defense by Isak Buhl-Mortensen

Title: One-point Functions in AdS/dCFT and Integrability

Abstract: Super Yang-Mills with a co-dimension one defect is studied, in particular, the field theory setup that arises in the D3-probe-D5 brane construction of the Karch-Randal idea. We look at the case where k ≥ 2 D3-branes are absorbed by the D5, giving rise to a domain wall defect that separates the field theory into an SU(N − k) theory and a broken SU(N) theory. The defect allows for interesting one-point functions in the SU(2) sub-sector already at tree-level. One-point functions in this sub-sector are computed, key results include the closed determinant formula at tree-level valid for all k, and subsequently a concise one-loop result for k = 2. The one-loop result is conjectured to be exact for the BMN vacuum. A major feat is the diagonalization of the bulk action around the fuzzy-funnel background, as it opens up for many novel tests of the AdS/dCFT correspondence. Results for the BMN one-point functions are compared with string theory in the double-scaling limit. Agreement is found at tree-level and subsequently an all loop conjecture is made based on integrability.