Finite-Temperature Conformal Field Theory Results for All Couplings: O(N) Model in 2+1 Dimensions

Area of Science:

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

Background:

• Gauge-gravity duality provides insights into strongly coupled quantum field theories.
• The entropy density of N=4 supersymmetric Yang-Mills theory serves as a benchmark.

Purpose of the Study:

• To analyze the entropy density of the massless O(N) model in 2+1 dimensions at finite temperature and varying couplings.
• To investigate the universality of physical quantities in bosonic conformal field theories.

Main Methods:

• Analytical solution of the O(N) model in the large N limit at finite temperature.
• Calculation of the retarded energy-momentum tensor correlator in the scalar channel.

Main Results:

• The entropy density decreases monotonically from the Stefan-Boltzmann limit (λ=0) to 4/5 of it at infinite coupling (λ=∞).
• The retarded energy-momentum tensor correlator exhibits two logarithmic branch cuts, not singularities, in the complex frequency plane.
• The 4/5 ratio and branch point locations are universal for a broad class of 2+1 dimensional bosonic conformal field theories.

Conclusions:

• The massless O(N) model in 2+1 dimensions displays universal behavior in its thermodynamic and dynamic properties.
• Findings contribute to understanding non-perturbative aspects of quantum field theories and potential connections to gravity.