One-Loop One-Point Functions in Gauge-Gravity Dualities with Defects

Area of Science:

• High-energy physics
• Quantum field theory
• String theory

Background:

• Investigating loop corrections to correlation functions in 4D defect conformal field theories (dCFTs).
• Focus on N=4 SYM theory with a codimension-one defect and differing SU(N) and SU(N-k) gauge groups.
• Holographic dual involves a D3-D5 probe brane system with AdS4×S2 geometry.

Purpose of the Study:

• To initiate the calculation of loop corrections to correlation functions in 4D dCFTs.
• To analyze the holographic dual of the D3-D5 probe brane system.
• To compare results with existing string theory computations.

Main Methods:

• Utilizing fuzzy-sphere coordinates to diagonalize the dCFT mass matrix.
• Reformulating x3-dependent mass terms as standard massive AdS4 propagators.
• Calculating one-loop corrections to one-point functions in the planar limit.

Main Results:

• Identified only two Feynman diagrams contributing to one-loop corrections for single-trace operators.
• Explicitly calculated the one-loop correction for the simplest chiral primary.
• Achieved perfect agreement with an earlier string-theory computation in a specific double scaling limit.

Conclusions:

• The study successfully initiated loop correction calculations in 4D dCFTs.
• The holographic approach provides a valid framework for these calculations.
• The methodology is discussed for generalization to various operators, finite N, and other observables like Wilson loops.