We present a two-loop field-theoretic analysis of incompressible helical magnetohydrodynamics (MHD) in fully developed stationary turbulence. A key feature of helical MHD is the appearance of an infrared-unstable “masslike” term in the loop diagrams of the magnetic response function. Physically, this term corresponds to the relevant perturbation of the Joule damping, proportional to $\mathbf{\nabla }\times \mathit{b}$ ($\mathit{b}=$ magnetic field). Its presence destabilizes the trivial ground state $\langle \mathit{b}\rangle =0$ and forces us to look for a mechanism for stabilizing the system. We show that such stabilization can be achieved in two ways: (i) by introducing into induction equation an external masslike parameter that precisely cancels these dangerous loop corrections (kinematic regime), or (ii) via spontaneous breaking of the rotational symmetry, leading to a new ground state with nonzero large-scale magnetic field (turbulent dynamo regime). For the latter case, we study the two-loop correction to the spontaneously generated magnetic field and demonstrate that Goldstone-like corrections to Alfvén modes along with some other anisotropic structures arise. Our results also confirm that the emergent mean magnetic field leads to a steeper slope of the magnetic energy spectrum, $-11/3+2{\gamma }_{b★}$ (with ${\gamma }_{b★}=-0.1039-0.4202{\rho }^2$, for $\left|\rho \right|⩽1$ as the degree of helicity), compared to the Kolmogorov velocity spectrum of $-11/3$, thereby breaking equipartition.

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• Dynamo theory
• Feynman diagrams
• Flow instability
• Fluctuations & noise
• Helicity
• Homogeneous turbulence
• Magnetohydrodynamic turbulence
• Magnetohydrodynamics
• Nonlinear dynamics in fluids
• Path integrals
• Perturbation theory
• Primordial magnetic fields
• Renormalization
• Renormalization group
• Spontaneous symmetry breaking
• Statistical field theory
• Galaxies
• Magnetic fluids
• Planets & planetary systems
• Stars
• Stochastic dynamical systems
• Continuous symmetries
• Parity
• Diagrammatic methods
• Path-integral methods
• Statistical hydrodynamics
• Stochastic differential equations