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The central charge of conformal field theories (CFTs) with defects decreases during renormalization group flows. This finding, using reflection positivity, applies to CFTs in dimensions d≥3 and planar boundaries in d=3.

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Area of Science:

  • Theoretical physics
  • High-energy physics
  • Condensed matter physics

Background:

  • Conformal field theories (CFTs) describe systems with scale invariance.
  • Defects in CFTs exhibit Weyl anomalies characterized by a central charge 'b'.
  • Renormalization group (RG) flows describe how physical systems change with energy scale.

Purpose of the Study:

  • To investigate the behavior of the central charge 'b' for CFTs with planar conformal defects under RG flow.
  • To establish a general principle for the evolution of defect central charges.

Main Methods:

  • Utilizing reflection positivity, a fundamental principle in quantum field theory.
  • Analyzing CFTs in dimensions d≥3 coupled to 2D conformal defects.
  • Considering CFTs in d=3 flat space with planar boundaries.

Main Results:

  • Demonstrated that the central charge 'b' must decrease or remain constant along defect RG flows.
  • The bulk CFT remains critical throughout the flow.
  • The result is applicable to both 2D defects in higher dimensions and planar boundaries in 3D.

Conclusions:

  • The defect central charge 'b' is a monotonic function of the RG flow, decreasing from UV to IR.
  • Reflection positivity provides a powerful tool for constraining anomalies and RG flow in CFTs with defects.
  • This work offers new insights into the behavior of quantum field theories with boundaries and defects.