How a-Type Anomalies Can Depend on Marginal Couplings

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.