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We introduce a generalized g theorem for line defects in conformal field theories (CFTs). This theorem proves that renormalization group (RG) flows on these defects are irreversible and possess a decreasing entropy function.

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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.
  • Renormalization group (RG) flows track changes in a system's parameters with scale.
  • Line defects introduce localized features within CFTs.

Purpose of the Study:

  • To generalize the g theorem to line defects in d-dimensional CFTs.
  • To investigate the properties of renormalization group (RG) flows on these line defects.
  • To establish the existence of a canonical decreasing entropy function for such flows.

Main Methods:

  • Analyzing constraints imposed by the ambient CFT on defect RG flows.
  • Developing a theoretical framework for irreversible RG flows on line defects.
  • Demonstrating the construction using a specific example of Wilson loops in four dimensions.

Main Results:

  • RG flows on line defects are shown to be irreversible.
  • A canonical decreasing entropy function is proven to exist for these flows.
  • The g theorem is successfully generalized to arbitrary dimensions for line defects.

Conclusions:

  • The generalized g theorem provides a powerful tool for studying defect CFTs.
  • The irreversibility of RG flows and the existence of a decreasing entropy function offer fundamental insights.
  • The findings have implications for understanding quantum field theories and their behavior in the presence of defects.