BCFT and OSFT moduli: an exact perturbative comparison

Starting from the pseudo-({mathcal {B}}_0) gauge solution for marginal deformations in OSFT, we analytically compute the relation between the perturbative deformation parameter (tilde{lambda }) in the solution and the BCFT marginal parameter (lambda ), up to fifth order, by evaluating the Ellwood invariants. We observe that the microscopic reason why (tilde{lambda }) and (lambda ) are different is that the OSFT propagator renormalizes contact-term divergences differently from the contour deformation used in BCFT.