Gauge Invariance at Large Charge

Area of Science:

• Quantum Field Theory
• High Energy Physics
• Condensed Matter Physics

Background:

• Large-charge expansion offers a semiclassical approach to quantum field theories with global symmetries.
• Generalizing this to gauge symmetries is challenging due to the difficulty in defining gauge-independent observables.

Purpose of the Study:

• To apply the large-charge expansion to calculate scaling dimensions of operators in the critical Abelian Higgs model.
• To address the challenge of defining gauge-independent observables in gauge theories.
• To provide a foundation for large-charge methods in gauge theories.

Main Methods:

• Employing the large-charge expansion to compute scaling dimensions to leading and next-to-leading orders in charge.
• Performing calculations in D=4-ε dimensions, considering all orders in the ε expansion.
• Comparing results with independent diagrammatic computations in the Landau gauge.

Main Results:

• Successfully calculated the scaling dimension of lowest-lying operators with U(1) charge Q.
• Demonstrated a match between large-charge expansion results and diagrammatic computations.
• Established an equivalence between gauge-independent dressed two-point functions and gauge-dependent ones in Landau gauge.

Conclusions:

• The large-charge expansion is a viable method for gauge theories, overcoming challenges with gauge independence.
• The study sheds light on defining gauge-independent exponents, resolving long-standing controversies.
• This work lays the groundwork for future applications of large-charge methods in gauge theories.