title: One-Loop One-Point Functions in Gauge-Gravity Dualities with Defects.
abstract: We initiate the calculation of loop corrections to correlation functions in 4D defect conformal field theories (dCFTs). More precisely, we consider N=4 SYM theory with a codimension-one defect separating two regions of space, x_{3}>0 and x_{3}<0, where the gauge group is SU(N) and SU(N-k), respectively. This setup is made possible by some of the real scalar fields acquiring a nonvanishing and x_{3}-dependent vacuum expectation value for x_{3}>0. The holographic dual is the D3-D5 probe brane system where the D5-brane geometry is AdS_{4}×S^{2} and a background gauge field has k units of flux through the S^{2}. We diagonalize the mass matrix of the dCFT making use of fuzzy-sphere coordinates and we handle the x_{3} dependence of the mass terms in the 4D Minkowski space propagators by reformulating these as standard massive AdS_{4} propagators. Furthermore, we show that only two Feynman diagrams contribute to the one-loop correction to the one-point function of any single-trace operator and we explicitly calculate this correction in the planar limit for the simplest chiral primary. The result of this calculation is compared to an earlier string-theory computation in a certain double scaling limit and perfect agreement is found. Finally, we discuss how to generalize our calculation to any single-trace operator, to finite N, and to other types of observables such as Wilson loops.
authors.affiliation: Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
authors.forename: Isak
authors.initials: I
authors.lastname: Buhl-Mortensen
authors.affiliation: Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
authors.forename: Marius
authors.initials: M
authors.lastname: de Leeuw
authors.affiliation: Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
authors.forename: Asger C
authors.initials: AC
authors.lastname: Ipsen
authors.affiliation: Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
authors.forename: Charlotte
authors.initials: C
authors.lastname: Kristjansen
authors.affiliation: Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
authors.forename: Matthias
authors.initials: M
authors.lastname: Wilhelm