Rolling in the Higgs Model and Elliptic Functions

Asymptotic methods in nonlinear dynamics are used to improve perturbation theory results in the oscillations regime. However, for some problems of nonlinear dynamics, particularly in the case of Higgs (Duffing) equation and the Friedmann cosmological equations, not only small oscillations regime is of interest but also the regime of rolling (climbing), more precisely the rolling from a top (climbing to a top). In the Friedman cosmology, where the slow rolling regime is often used, the rolling from a top (not necessary slow) is of interest too. In the present work a method for approximate solution to the Higgs equation in the rolling regime is presented. It is shown that in order to improve perturbation theory in the rolling regime turns out to be effective not to use an expansion in trigonometric functions as it is done in case of small oscillations but use expansions in hyperbolic functions instead. This regime is investigated using the representation of the solution in terms of elliptic functions. An accuracy of the corresponding approximation is estimated.Comment: Latex, 36 Pages, 8 figures, typos correcte

Descent Relations and Oscillator Level Truncation Method

We reexamine the oscillator level truncation method in the bosonic String Field Theory (SFT) by calculation the descent relation =Z_3<V_2|. For the ghost sector we use the fermionic vertices in the standard oscillator basis. We propose two new schemes for calculations. In the first one we assume that the insertion satisfies the overlap equation for the vertices and in the second one we use the direct calculations. In both schemes we get the correct structures of the exponent and pre-exponent of the vertex <V_2|, but we find out different normalization factors Z_3.Comment: 21 pages, 10 figures, Late

Dimension two vacuum condensates in gauge-invariant theories

Gauge dependence of the dimension two condensate in Abelian and non-Abelian Yang-Mills theory is investigated.Comment: 10 page

On Gauge Equivalence of Tachyon Solutions in Cubic Neveu-Schwarz String Field Theory

Simple analytic solution to cubic Neveu-Schwarz String Field Theory including the $GSO(-)$ sector is presented. This solution is an analog of the Erler-Schnabl solution for bosonic case and one of the authors solution for the pure $GSO(+)$ case. Gauge transformations of the new solution to others known solutions for the $NS$ string tachyon condensation are constructed explicitly. This gauge equivalence manifestly supports the early observed fact that these solutions have the same value of the action density.Comment: 8 pages, LaTe

Quantum field theory on manifolds with a boundary

We discuss quantum theory of fields \phi defined on (d+1)-dimensional manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(\phi) which is a bilinear form in \phi defines the Gaussian measure with a covariance (Green function) {\cal G}. We discuss a relation between the quantum field theory with a fixed boundary condition \Phi and the theory defined by the Green function {\cal G}. It is shown that the latter results by an average over \Phi of the first. The QFT in (anti)de Sitter space is treated as an example. It is shown that quantum fields on the boundary are more regular than the ones on (anti) de Sitter space.Comment: The version to appear in Journal of Physics A, a discussion on the relation to other works in the field is adde

Witten's Vertex Made Simple

The infinite matrices in Witten's vertex are easy to diagonalize. It just requires some SL(2,R) lore plus a Watson-Sommerfeld transformation. We calculate the eigenvalues of all Neumann matrices for all scale dimensions s, both for matter and ghosts, including fractional s which we use to regulate the difficult s=0 limit. We find that s=1 eigenfunctions just acquire a p term, and x gets replaced by the midpoint position.Comment: 24 pages, 2 figures, RevTeX style, typos correcte

Aspects of Open-Closed Duality in a Background B-Field II

It was shown in [hep-th/0503009], in the context of bosonic theory that the IR singular terms that arise as a result of integrating out high momentum modes in nonplanar diagrams of noncommutative gauge theory can be recovered from low lying tree-level closed string exchanges. This follows as a natural consequence of world-sheet open-closed string duality. Here using the same setup we study the phenomenon for noncommutative ${\cal N}=2$ gauge theory realised on a $D_3$ fractional brane localised at the fixed point of $C^2/Z_2$. The IR singularities from the massless closed string exchanges are exactly equal to those coming from one-loop gauge theory. This is as a result of cancellation of all contributions from the massive modes.Comment: 27 pages, 1 figure, references added, typos correcte

Aspects of Open-Closed Duality in a Background B-Field

We study closed string exchanges in background $B$-field. By analysing the two point one loop amplitude in bosonic string theory, we show that tree-level exchange of lowest lying, tachyonic and massless closed string modes, have IR singularities similar to those of the nonplanar sector in noncommutative gauge theories. We further isolate the contributions from each of the massless modes. We interpret these results as the manifestation of open/closed string duality, where the IR behaviour of the boundary noncommutative gauge theory is reconstructed from the bulk theory of closed strings.Comment: 33 pages, 4 figures, v2:references added, v3: minor changes, typos corrected, references adde

Non-extremal Localised Branes and Vacuum Solutions in M-Theory

Non-extremal overlapping p-brane supergravity solutions localised in their relative transverse coordinates are constructed. The construction uses an algebraic method of solving the bosonic equations of motion. It is shown that these non-extremal solutions can be obtained from the extremal solutions by means of the superposition of two deformation functions defined by vacuum solutions of M-theory. Vacuum solutions of M-theory including irrational powers of harmonic functions are discussed.Comment: LaTeX, 16 pages, no figures, typos correcte

Semiclassical properties and chaos degree for the quantum baker's map

We study the chaotic behaviour and the quantum-classical correspondence for the baker's map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic timescale. The quantum chaos degree is computed and it is demonstrated that it describes the chaotic features of the model. The correspondence between classical and quantum chaos degrees is considered.Comment: 30 pages, 4 figures, accepted for publication in J. Math. Phy