Solving conformal defects in 3D conformal field theory using fuzzy sphere regularization

Area of Science:

• Theoretical Physics
• High Energy Physics
• Condensed Matter Physics

Background:

• Defects in conformal field theories (CFTs) are crucial but challenging to study, especially in higher dimensions.
• Existing methods for analyzing defects in 3D CFTs present significant difficulties.

Purpose of the Study:

• To demonstrate the utility of fuzzy sphere regularization for analyzing defects in 3D CFTs.
• To investigate the magnetic line defect in the 3D Ising CFT and its properties.

Main Methods:

• Application of the fuzzy (non-commutative) sphere regularization technique.
• Analysis of the magnetic line defect within the 3D Ising CFT framework.
• Utilizing the state-operator correspondence to extract operator scaling dimensions.

Main Results:

• The magnetic line defect in the 3D Ising CFT was shown to flow to a conformal defect fixed point.
• Six low-lying defect primary operators, including the displacement operator, were identified and their scaling dimensions accurately extracted.
• One-point bulk and two-point bulk-defect correlators were computed, showing agreement with defect conformal symmetry predictions.

Conclusions:

• Fuzzy sphere regularization provides a transparent and powerful method for studying 3D defect CFTs.
• The study successfully analyzed a specific defect in the 3D Ising CFT, yielding key insights into its behavior and associated operators.
• The findings highlight the potential of this theoretical scheme for exploring complex defect physics in higher-dimensional CFTs.