7 research outputs found
Functions holomorphic along holomorphic vector fields
The main result of the paper is the following generalization of Forelli's
theorem: Suppose F is a holomorphic vector field with singular point at p, such
that F is linearizable at p and the matrix is diagonalizable with the
eigenvalues whose ratios are positive reals. Then any function that has
an asymptotic Taylor expansion at p and is holomorphic along the complex
integral curves of F is holomorphic in a neighborhood of p.
We also present an example to show that the requirement for ratios of the
eigenvalues to be positive reals is necessary
Bouncing and Accelerating Solutions in Nonlocal Stringy Models
A general class of cosmological models driven by a non-local scalar field
inspired by string field theories is studied. In particular cases the scalar
field is a string dilaton or a string tachyon. A distinguished feature of these
models is a crossing of the phantom divide. We reveal the nature of this
phenomena showing that it is caused by an equivalence of the initial non-local
model to a model with an infinite number of local fields some of which are
ghosts. Deformations of the model that admit exact solutions are constructed.
These deformations contain locking potentials that stabilize solutions.
Bouncing and accelerating solutions are presented.Comment: Minor corrections, references added, published in JHE
Cosmological perturbations in SFT inspired non-local scalar field models
We study cosmological perturbations in models with a single non-local scalar
field originating from the string field theory description of the rolling
tachyon dynamics. We construct the equation for the energy density
perturbations of the non-local scalar field and explicitly prove that for the
free field it is identical to a system of local cosmological perturbation
equations in a particular model with multiple (maybe infinitely many) local
free scalar fields.Comment: 21 pages, no figures, v3: presentation improved, results unchanged,
references adde