Related papers: Harrison--Zeldovich spectrum from conformal invari…
Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The complete particle spectrum of the low-energy, four-dimensional theory is specified by the…
The spectrum of nonabelian gauge theories cannot be described in terms of elementary particles, and so must be constructed from gauge-invariant composite operators, even in the presence of a Brout--Englert--Higgs effect. This leads to…
We describe a novel mechanism to seed a nearly scale invariant spectrum of adiabatic perturbations during a non-inflationary stage. It relies on a modified dispersion relation that contains higher powers of the spatial momentum of matter…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation…
For any Lipschitz domain we construct an arbitrarily small, localized perturbation which splits the spectrum of the Laplacian into simple eigenvalues. We use for this purpose a Hadamard's formula and spectral stability results.
In a recent paper arXiv:0910.2230, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the…
In this lecture we outline the main results of our investigations of certain field-theoretic systems which have V-shaped field potential. After presenting physical examples of such systems, we show that in static problems the exact ground…
Cosmological perturbations, originating in the quantum fluctuations of the fields that drive inflation, are observed to be nearly scale invariant at the largest scales. At smaller scales, however, perturbations are not severely constrained…
The variational formulation for Lie-transform Hamiltonian perturbation theory is presented in terms of an action functional defined on a two-dimensional parameter space. A fundamental equation in Hamiltonian perturbation theory is shown to…
We investigate the moduli space of conformal field theories by setting up a canonical mathematical process for exponentiating perturbations corresponding to critical fields. We apply this process to the free field theory and the Gepner…
In ${\cal PT}-$symmetric quantum mechanics one of the most characteristic mathematical features of the formalism is the explicit Hamiltonian-dependence of the physical Hilbert space of states ${\cal H}={\cal H}(H)$. Some of the most…
We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…
We discuss non-Hermitian field theories where the spectrum of the Hamiltonian involves only real energies. We make three observations. (i) The theories obtained from supersymmetric theories by nonanticommutative deformations belong in many…
We present a bouncing cosmology which evolves from the contracting to the expanding phase in a smooth way, without developing instabilities or pathologies and remaining in the regime of validity of 4d effective field theory. A nearly scale…
We focus our attention on the one dimensional scalar theories that result from dimensionally reducing the free scalar field theory in arbitrary d dimensions. As is well known, after integrating out the angular coordinates, the free scalar…
A four dimensional scalar field theory with quartic and of higher power interactions suffers the triviality issue at the quantum level. This is due to coupling constants that, contrary to the physical expectations, seem to grow without a…
Low energy effective field theories motivated by string theory will likely contain several scalar moduli fields which will be relevant to early Universe cosmology. Some of these fields are expected to couple with non-standard kinetic terms…
We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on…
In this paper, we have studied the spectrum of curvature perturbation of multi-field inflation with general small-field potential. We assume that the isocurvature perturbation may be neglected, and by using the Sasaki-Stewart formalism, we…
We describe the fully gauge invariant cosmological perturbation equations in teleparallel gravity by using the gauge covariant version of the Stewart lemma for obtaining the variations in tetrad perturbations. In teleparallel theory,…