3,891 research outputs found
Vector Field and Inflation
We have investigated if the vector field can give rise to an accelerating
phase in the early universe. We consider a timelike vector field with a general
quadratic kinetic term in order to preserve an isotropic background spacetime.
The vector field potential is required to satisfy the three minimal conditions
for successful inflation: i) , ii) and iii) the slow-roll
conditions. As an example, we consider the massive vector potential and small
field type potential as like in scalar driven inflation.Comment: 1+7pages, 3figures, To appear in the Proceedings of the CospA 2008,
Kore
The MacMahon R-matrix
We introduce an -matrix acting on the tensor product of MacMahon
representations of Ding-Iohara-Miki (DIM) algebra
. This -matrix acts on pairs
of Young diagrams and retains the nice symmetry of the DIM algebra under
the permutation of three deformation parameters , and
. We construct the intertwining operator for a tensor product of
the horizontal Fock representation and the vertical MacMahon representation and
show that the intertwiners are permuted using the MacMahon -matrix.Comment: 39 page
Anisotropic Power-law Inflation
We study an inflationary scenario in supergravity model with a gauge kinetic
function. We find exact anisotropic power-law inflationary solutions when both
the potential function for an inflaton and the gauge kinetic function are
exponential type. The dynamical system analysis tells us that the anisotropic
power-law inflation is an attractor for a large parameter region.Comment: 14 pages, 1 figure. References added, minor corrections include
Higher-dimensional WZW Model on K\"ahler Manifold and Toroidal Lie Algebra
We construct a generalization of the two-dimensional Wess-Zumino-Witten model
on a -dimensional K\"ahler manifold as a group-valued non-linear sigma
model with an anomaly term containing the K\"ahler form. The model is shown to
have an infinite-dimensional symmetry which generates an -toroidal Lie
algebra. The classical equation of motion turns out to be the
Donaldson-Uhlenbeck-Yau equation, which is a -dimensional generalization of
the self-dual Yang-Mills equation.Comment: 12 pages, Late
Anisotropic Inflation from Charged Scalar Fields
We consider models of inflation with U(1) gauge fields and charged scalar
fields including symmetry breaking potential, chaotic inflation and hybrid
inflation. We show that there exist attractor solutions where the anisotropies
produced during inflation becomes comparable to the slow-roll parameters. In
the models where the inflaton field is a charged scalar field the gauge field
becomes highly oscillatory at the end of inflation ending inflation quickly.
Furthermore, in charged hybrid inflation the onset of waterfall phase
transition at the end of inflation is affected significantly by the evolution
of the background gauge field. Rapid oscillations of the gauge field and its
coupling to inflaton can have interesting effects on preheating and
non-Gaussianities.Comment: minor changes, references added, figures are modified, conforms JCAP
published versio
Macdonald operators and homological invariants of the colored Hopf link
Using a power sum (boson) realization for the Macdonald operators, we
investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the
homological invariants of the colored Hopf link, which include
Khovanov-Rozansky homology as a special case. We prove the polynomiality of the
invariants obtained by GIKV's proposal for arbitrary representations. We derive
a closed formula of the invariants of the colored Hopf link for antisymmetric
representations. We argue that a little amendment of GIKV's proposal is
required to make all the coefficients of the polynomial non-negative integers.Comment: 31 pages. Published version with an additional appendi
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