jaxvacua.conifold.zcf_solver.W_log_coeff

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jaxvacua.conifold.zcf_solver.W_log_coeff#

W_log_coeff(self, z, tau, flux, mode='manual', conj=False)#

Public dispatcher for the regular \(O(z_{\rm cf}^0)\) coefficient \(\widetilde W_1\) of \(\partial_{z_{\rm cf}} W_{\rm coni}\) near the conifold.

The F-term equation reads log_prefactor · ln(-2πi·z_cf) + W_log_coeff + O(z_cf) = 0, so the leading-order solution is z_cf = -(1/2πi) · exp(-W_log_coeff / log_prefactor).

Parameters:

  • z – bulk moduli (h12-1 complex components).

  • tau – axio-dilaton.

  • flux – full flux vector.

  • mode – "manual" for the closed-form kappa / a_matrix / b_vector + Li assembly; "autodiff" for the assembly via the css-side F_coniLCS_exp + dF_coniLCS_exp helpers (manual and autodiff agree numerically — cross-checked in the smoke test); "pfv" for the PFV / linear-racetrack approximation, which uses only the integer fluxes and does NOT agree with manual/autodiff (it’s a deliberate approximation that becomes exact at the racetrack-stationary point).

  • conj – take complex-conjugate branch.

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