  We derive an effective field theory (EFT) for cosmological Lyman alpha forest
fluctuations valid for the power spectrum at the one-loop order. The
``bottom-up'' EFT expansion at the level of the transmitted flux is identical
to the line-of-sight dependent bias model first derived by Desjacques et al. We
confirm this result by a ``top-down'' derivation based on the exponential map
of the optical depth field. Specifically, we show that the combination of the
exponential map and conditions of renormalizability generates the same EFT
expansion as the ``bottom-up'' approach. In passing, we point out
inconsistencies of the tree-level perturbative expansion of the exponential map
without counterterms. To facilitate practical applications, we generalize the
FFTLog method for efficient calculations of one-loop integrals from new
line-of-sight dependent operators. Finally, we compare the one-loop EFT model
against data from the Sherwood hydrodynamic simulation. The theory fits the
data with sub percent accuracy up to $k= $ 3 $h$Mpc$^{-1}$ at $z= 2.8$ for both
3D and 1D correlations. Our model can be readily used for cosmological
full-shape analyses of Lyman alpha forest data.
