Conformal Dimensions in the Large Charge Sectors at the O(4) Wilson-Fisher Fixed Point

Area of Science:

• High-energy physics
• Condensed matter theory
• Quantum field theory

Background:

• The O(4) Wilson-Fisher fixed point is crucial for understanding critical phenomena in 2+1 dimensions.
• Investigating large-charge sectors provides insights into universal behavior near critical points.

Purpose of the Study:

• To derive a formula for conformal dimensions in fixed large-charge sectors of the O(4) Wilson-Fisher fixed point.
• To computationally verify the derived formula and determine key theoretical constants.

Main Methods:

• Utilized effective field theory to derive analytical predictions for conformal dimensions.
• Employed Monte Carlo simulations on a discrete lattice formulation of the O(4) field theory.
• Focused on sectors with equal large spins (j_{L}=j_{R}) for computational tractability.

Main Results:

• Derived a formula D(j_{L},j_{R}) for conformal dimensions dependent on two constants, c_{3/2} and c_{1/2}.
• Monte Carlo calculations showed excellent agreement with the theoretical formula.
• Estimated the constants: c_{3/2} = 1.068(4) and c_{1/2} = 0.083(3).

Conclusions:

• The study successfully connects theoretical predictions from effective field theory with numerical results from lattice simulations.
• The derived formula and computed constants offer valuable parameters for characterizing the O(4) Wilson-Fisher fixed point in 2+1 dimensions.