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This is a Quantitative Study study.

October 20, 2025Open Access

Phase Transitions at Unusual Values of θ

Key Points

Phase transitions occur at unusual values of θ, with transitions expected at θ=π for N_F=0.
At N_F=1,2,3, we observe phase transitions at fractional values of π, demonstrating unique vacuum behavior.
The approach involves analyzing supersymmetric gauge theory under conditions ensuring the validity of IR analysis.
This analysis highlights the importance of θ dependence in the structure of vacuum energy in gauge theories.

Abstract

We calculate the θ dependence in a cousin of QCD, where the vacuum structure can be analyzed exactly. The theory is N=2 SU (2) gauge theory with NF=0, 1, 2, 3 flavors of fundamentals, explicitly broken to N=1 via an adjoint superpotential, and coupled to anomaly mediated supersymmetry breaking (AMSB). The hierarchy m₀₌ₒ₁ μ₍=₁ Λ ensures the validity of our IR analysis. As expected from ordinary QCD, the vacuum energy is a function of θ which undergoes 1st order phase transitions between different vacua where the various dyons condense. For NF=0 we find the expected phase transition at θ=π, while for NF=1, 2, 3 we find phase transitions at fractional values of π.

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