Exact RG Flow (Wilson–Polchinski)

Wilsonian effective action flowing through theory space under mode elimination

g₁ = 0.00   g₂ = 0.00
Wilson–Polchinski exact RG integrates out high-momentum modes, generating a flow in the space of all couplings. Fixed points correspond to scale-invariant theories: the Gaussian (origin, free field) and Wilson–Fisher (interacting critical point). Arrows show the beta-function vector field. Relevant operators grow away from the fixed point; irrelevant operators flow back. The separatrix between basins is the renormalized trajectory — the universality class boundary. Click canvas to place a new trajectory.