# BCFT and OSFT moduli: an exact perturbative comparison

## TL;DR

This paper analytically compares the perturbative parameters of marginal deformations in open string field theory and boundary conformal field theory, revealing how different regularization methods affect their relation.

## Contribution

It provides an exact fifth-order perturbative calculation of the relation between OSFT and BCFT marginal parameters, highlighting the impact of propagator renormalization.

## Key findings

- The OSFT and BCFT marginal parameters differ due to distinct regularization schemes.
- The relation between parameters is computed analytically up to fifth order.
- Contact term divergences are renormalized differently in OSFT and BCFT.

## Abstract

Starting from the pseudo-${\cal B}_0$ 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