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Even dimensional defects and boundaries in conformal field theory exhibit type A anomalies. Their one-point functions are anomalous, linked to the a anomaly

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Area of Science:

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

Background:

  • Conformal field theories (CFTs) are crucial in understanding critical phenomena and quantum gravity.
  • Defects and boundaries introduce rich structures and anomalies in quantum field theories.
  • Type A anomalies are topological quantum effects that appear in certain quantum field theories.

Purpose of the Study:

  • To investigate the nature of anomalies on defects and boundaries in even-dimensional conformal field theories.
  • To analyze the one-point functions of marginal operators in the presence of these defects and boundaries.
  • To establish a relationship between these anomalous one-point functions and the a anomaly.

Main Methods:

  • Calculation of one-point functions for marginal operators in CFTs with defects and boundaries.
  • Application of the Wess-Zumino consistency condition.
  • Analysis of the dependence of the constant term F on marginal parameters for odd-dimensional surfaces.

Main Results:

  • Even-dimensional defects and boundaries in CFTs support type A anomalies on their world volumes.
  • One-point functions of marginal operators are shown to be anomalous in the presence of defects and boundaries.
  • The Wess-Zumino consistency condition reveals a relationship between anomalous one-point functions and the derivative of the a anomaly with respect to marginal coupling.
  • The constant term F for odd-dimensional surfaces can depend on marginal parameters.

Conclusions:

  • Anomalies on defects and boundaries are a fundamental feature of even-dimensional CFTs.
  • The interplay between marginal operators, defects, and the a anomaly is precisely described by the Wess-Zumino consistency condition.
  • The behavior of surface terms in odd dimensions highlights the sensitivity of these anomalies to the underlying theory's parameters.