Speaker
Description
We study a stochastic version of magnetohydrodynamics (MHD) formulated as the generalized A-model of a passively advected vector field with full back-reaction on the flow. The model includes parity breaking via a helicity parameter ρ and a continuous interaction parameter A that interpolates between important physical limits (A = 1 for MHD, A = 0 for passive vector advection). Using the field-theoretic renormalization-group approach and the ε-expansion, we perform a two-loop calculation of the renormalization constants that govern the magnetic-field sector and focus in particular on the three-point vertex $Γ_{v′bb}$ and the associated constant $Z_3$. The one-loop structure is recovered and extended to arbitrary A, while the two-loop pole structure is evaluated numerically. For the physically relevant three-dimensional MHD case (A = 1) we obtain an explicit two-loop contribution to the magnetic anomalous dimension which depends on helicity as $c_{2,1}^{A=1} = C(3) [0.201432 + ρ²·0.288499]$ (with $C(3)=1/(480π⁴)$), demonstrating a nontrivial $\rho^2$ dependence at this order. These results advance multiloop RG treatments of dynamo-type effects and provide groundwork for future studies of scaling and anomalous exponents in helical MHD turbulence.
