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1. Lattice Gauge Theory

   Linked via "Hadronic Manifold Embedding (HME)"

   where $\Theta(P)$ is the phase angle dependent on the gauge configuration $P$. For standard Monte Carlo methods, averaging over configurations where the integrand oscillates requires sampling weighted by $|\det(M_F)|$, leading to exponentially large statistical variance as the system volume or imaginary time extent grows.
   Research efforts have explored Complex Langevin dynamics, stochastic quantization, and the specialized **[Hadronic Manifold Embedding (HME)](/entries/hadronic-man…