What is this EGBd model and how it fits in the grand scheme of things of string theory?
The EGBd (dilatonic Einstein-Gauss-Bonnet) model is a low-energy approximation to a particular variant of string theory. This approximation is roughly similar to General Relativity (GR). In GR the geometry of empty space is solely determined by a particular mathematical representation of the curvature of spacetime. In EGBd the geometry of empty space is determined additionally by a different mathematical representation of the curvature of spacetime (the Gauss-Bonnet term) and by a scalar field (the dilaton field).
Background: The Gauss-Bonnet term is precisely zero, if spacetime is assumed to have 4 dimensions. It was shown a few years ago that in 5 dimensions the non-zero Gauss-Bonnet term mimics exotic matter (needed to prevent wormhole collapse) and permits traversable wormholes (in 5D).
This paper purports to show that a EGBd allows traversable wormholes in 4 dimensions.
My problem with the paper is that it assumes that the kinetic energy of the dilaton field is manifestly negative. This is contrary to the manifestly positive kinetic energy of the dilaton field in the usual Gauss-Bonnet-dilatonic low-energy approximation to string theory. It shouldn't be too surprising that a theory that is similar to GR except that it contains a field with negative kinetic energy (and a probably zero or negligibly important Gauss-Bonnet term) would permit traversable wormholes in 4D (because the negative-energy matter needed to hold open wormholes in built right into the theory).
is this fringe science or is serious?
It's serious, but unimportant. Assuming there are no mistakes in the paper, it's upshot is this: If a theory for which there is not a shred of experimental evidence (string theory) is true, then traversable wormholes are possible in 4D without the need of a separate source of exotic (negative-energy) matter.