24 research outputs found
Stable Exact Solutions in Cosmological Models with Two Scalar Fields
The stability of isotropic cosmological solutions for two-field models in the
Bianchi I metric is considered. We prove that the sufficient conditions for the
Lyapunov stability in the Friedmann-Robertson-Walker metric provide the
stability with respect to anisotropic perturbations in the Bianchi I metric and
with respect to the cold dark matter energy density fluctuations. Sufficient
conditions for the Lyapunov stability of the isotropic fixed points of the
system of the Einstein equations have been found. We use the superpotential
method to construct stable kink-type solutions and obtain sufficient conditions
on the superpotential for the Lyapunov stability of the corresponding exact
solutions. We analyze the stability of isotropic kink-type solutions for string
field theory inspired cosmological models.Comment: 23 pages, v3:typos corrected, references adde
On Modified Gravity
We consider some aspects of nonlocal modified gravity, where nonlocality is
of the type . In particular, using ansatz of the form
we find a few solutions for the spatially flat
FLRW metric. There are singular and nonsingular bounce solutions. For late
cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is
decelerated. R (t) = 0 satisfies all equations when k = -1.Comment: added references; made some clarifications; 8 page
Higher Derivative CP(N) Model and Quantization of the Induced Chern-Simons Term
We consider higher derivative CP(N) model in 2+1 dimensions with the
Wess-Zumino-Witten term and the topological current density squared term. We
quantize the theory by using the auxiliary gauge field formulation in the path
integral method and prove that the extended model remains renormalizable in the
large N limit. We find that the Maxwell-Chern-Simons theory is dynamically
induced in the large N effective action at a nontrivial UV fixed point. The
quantization of the Chern-Simons term is also discussed.Comment: 8 pages, no figure, a minor change in abstract, added Comments on the
quantization of the Chern-Simons term whose coefficient is also corrected,
and some references are added. Some typos are corrected. Added a new
paragraph checking the equivalence between (3) and (5), and a related
referenc
On the center-vortex baryonic area law
We correct an unfortunate error in an earlier work of the author, and show
that in center-vortex QCD (gauge group SU(3)) the baryonic area law is the
so-called law, described by a minimal area with three surfaces spanning the
three quark world lines and meeting at a central Steiner line joining the two
common meeting points of the world lines. (The earlier claim was that this area
law was a so-called law, involving three extremal areas spanning the
three pairs of quark world lines.) We give a preliminary discussion of the
extension of these results to . These results are based on the
(correct) baryonic Stokes' theorem given in the earlier work claiming a
law. The -form area law for SU(3) is in agreement with the most
recent lattice calculations.Comment: 5 pages, RevTeX4, 5 .eps figure
Solitons in a Grassmannian sigma-model Coupled to Chern-Simons Term
We propose an exactly solvable Grassmannian sigma-model coupled to the
Chern-Simons theory. In the presence of a novel topological term our model
admits exact self-dual vortex solutions which are identical to those of pure
Grassmannian model, but the topological charge has a physical meaning as a
magnetic flux since the gauge field is no longer auxiliary. We also extend the
theory to a noncommutative plane and analyze the BPS solutions.Comment: 10+1 pages, No figure, LaTeX; Reference added, Minor changes, to
appear in Phys. Rev.
Renormalization group and 1/N expansion for 3-dimensional Ginzburg-Landau-Wilson models
A renormalization-group scheme is developed for the 3-dimensional
O()-symmetric Ginzburg-Landau-Wilson model, which is consistent with the
use of a 1/N expansion as a systematic method of approximation. It is motivated
by an application to the critical properties of superconductors, reported in a
separate paper. Within this scheme, the infrared stable fixed point controlling
critical behaviour appears at , where is the inverse of
the quartic coupling constant, and an efficient renormalization procedure
consists in the minimal subtraction of ultraviolet divergences at . This
scheme is implemented at next-to-leading order, and the standard results for
critical exponents calculated by other means are recovered. An apparently novel
result of this non-perturbative method of approximation is that corrections to
scaling (or confluent singularities) do not, as in perturbative analyses,
appear as simple power series in the variable . At least in
three dimensions, the power series are modified by powers of .Comment: 20 pages; 5 figure
Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations
We describe an infinite-dimensional algebra of hidden symmetries of N=4
supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a
generalization of the supertwistor correspondence. Using the latter, we
construct an infinite sequence of flows on the solution space of the N=4 SYM
equations. The dependence of the SYM fields on the parameters along the flows
can be recovered by solving the equations of the hierarchy. We embed the N=4
SYM equations in the infinite system of the hierarchy equations and show that
this SYM hierarchy is associated with an infinite set of graded symmetries
recursively generated from supertranslations. Presumably, the existence of such
nonlocal symmetries underlies the observed integrable structures in quantum N=4
SYM theory.Comment: 24 page
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
The universe formation by a space reduction cascade with random initial parameters
In this paper we discuss the creation of our universe using the idea of extra
dimensions. The initial, multidimensional Lagrangian contains only metric
tensor. We have found many sets of the numerical values of the Lagrangian
parameters corresponding to the observed low-energy physics of our universe.
Different initial parameters can lead to the same values of fundamental
constants by the appropriate choice of a dimensional reduction cascade. This
result diminishes the significance of the search for the 'unique' initial
Lagrangian. We also have obtained a large number of low-energy vacua, which is
known as a 'landscape' in the string theory.Comment: 17 pages, 1 figur
p-Adic Mathematical Physics
A brief review of some selected topics in p-adic mathematical physics is
presented.Comment: 36 page