The analytic structure of the fixed charge expansion

Area of Science:

• Theoretical Physics
• Quantum Field Theory

Background:

• The fixed charge expansion is a key tool for studying conformal field theories (CFTs).
• Understanding analytic properties of this expansion is crucial for various dimensions.

Purpose of the Study:

• To investigate the analytic properties of the fixed charge expansion for O(N) and QED3 CFTs in different spacetime dimensions.
• To analyze the behavior of conformal dimensions in double scaling limits.

Main Methods:

• Fixed charge expansion
• Resurgence techniques
• Analysis in d = 3 - ε and d = 4 - ε dimensions

Main Results:

• In d = 3 - ε dimensions, O(N) conformal dimensions are non-Borel summable and doubly factorial divergent, linked to worldline instantons.
• In d = 4 - ε dimensions, corrections lead to a convergent series with a new branch cut singularity, impacting O(N) stability for negative ε.
• QED3 exhibits Borel summable, single factorial divergent dimensions at leading order in the large N limit.

Conclusions:

• The analytic properties of the fixed charge expansion differ significantly between 3 and 4 spacetime dimensions.
• Resurgence techniques connect singularities to instantons, providing deeper insights into CFT behavior.
• The stability of the O(N) large charge sector is sensitive to dimensionality and epsilon values.