Non-perturbative calculations for the effective potential of the PTPT symmetric and non-Hermitian (−gϕ4)(-g\phi^{4}) field theoretic model

We investigate the effective potential of the $PT$ symmetric $(-g\phi^{4})$ field theory, perturbatively as well as non-perturbatively. For the perturbative calculations, we first use normal ordering to obtain the first order effective potential from which the predicted vacuum condensate vanishes exponentially as $G\to G^+$ in agreement with previous calculations. For the higher orders, we employed the invariance of the bare parameters under the change of the mass scale $t$ to fix the transformed form totally equivalent to the original theory. The form so obtained up to $G^3$ is new and shows that all the 1PI amplitudes are perurbative for both $G\ll 1$ and $G\gg 1$ regions. For the intermediate region, we modified the fractal self-similar resummation method to have a unique resummation formula for all $G$ values. This unique formula is necessary because the effective potential is the generating functional for all the 1PI amplitudes which can be obtained via $\partial^n E/\partial b^n$ and thus we can obtain an analytic calculation for the 1PI amplitudes. Again, the resummed from of the effective potential is new and interpolates the effective potential between the perturbative regions. Moreover, the resummed effective potential agrees in spirit of previous calculation concerning bound states.Comment: 20 page

On supergravity solutions of space-like Dp-branes

Recently the time dependent solutions of type II supergravities in $d = 10$, with the metric having the symmetry $ISO(p+1) \times SO(8-p, 1)$ have been given by two groups (Chen-Gal'tsov-Gutperle (CGG), [hep-th/0204071] and Kruczenski-Myers-Peet (KMP), [hep-th/0204144]). The supergravity solutions correspond to space-like D$p$-branes in type II string theory. While the CGG solution is a four parameter solution, the KMP solution is a three parameter solution and so in general they are different. This difference can be attributed to the fact that unlike the CGG solution, KMP uses a specific boundary condition for the metric and the dilaton field. It is shown that when we impose the boundary conditions used in the KMP solution to the CGG solution then both become three parameter solutions and they map to each other under a coordinate transformation along with a Hodge duality of the field strength. We also give the relations between the parameters characterizing the two solutions.Comment: 14 pages, LaTeX, v2: minor corrections and a reference adde

On the symmetries of special holonomy sigma models

In addition to superconformal symmetry, (1,1) supersymmetric two-dimensional sigma models on special holonomy manifolds have extra symmetries that are in one-to-one correspondence with the covariantly constant forms on these manifolds. The superconformal algebras extended by these symmetries close as W-algebras, i.e. they have field-dependent structure functions. It is shown that it is not possible to write down cohomological equations for potential quantum anomalies when the structure functions are field-dependent. In order to do this it is necessary to linearise the algebras by treating composite currents as generators of additional symmetries. It is shown that all cases can be linearised in a finite number of steps, except for G_2 and SU(3). Additional problems in the quantisation procedure are briefly discussed.Comment: 16 pages. Abstract improved and a few typographical errors correcte

New Realisations of Minimal Models and the Structure of W-Strings

The quantization of a free boson whose momentum satisfies a cubic constraint leads to a c=\ha conformal field theory with a BRST symmetry. The theory also has a $W_\infty$ symmetry in which all the generators except the stress-tensor are BRST-exact and so topological. The BRST cohomology includes states of conformal dimensions 0,\si,\ha, together with \lq copies' of these states obtained by acting with picture-changing and screening operators. The 3-point and 4-point correlation functions agree with those of the Ising model, suggesting that the theory is equivalent to the critical Ising model. At tree level, the $W_3$ string can be viewed as an ordinary $c=26$ string whose conformal matter sector includes this realisation of the Ising model. The two-boson $W_3$ string is equivalent to the Ising model coupled to two-dimensional quantum gravity. Similar results apply for other W-strings and minimal models.Comment: 28 pages, NSF-ITP-93-65, QMW-93-1

Static, non-SUSY pp-branes in diverse dimensions

We give explicit constructions of static, non-supersymmetric $p$-brane (for $p \leq d-4$, where $d$ is the space-time dimensionality and including $p=-1$ or D-instanton) solutions of type II supergravities in diverse dimensions. A subclass of these are the static counterpart of the time dependent solutions obtained in [hep-th/0309202]. Depending on the forms of the non-extremality function $G(r)$ defined in the text, we discuss various possible solutions and their region of validity. We show how one class of these solutions interpolate between the $p$-brane--anti $p$-brane solutions and the usual BPS $p$-brane solutions in $d=10$, while the other class, although have BPS limits, do not have such an interpretation. We point out how the time dependent solutions mentioned above can be obtained by a Wick rotation of one class of these static solutions. We also discuss another type of solutions which might seem non-supersymmetric, but we show by a coordinate transformation that they are nothing but the near horizon limits of the various BPS $p$-branes already known.Comment: 29 pages, typos corrected, references adde

Intersecting S-Brane Solutions of D=11 Supergravity

We construct all possible orthogonally intersecting S-brane solutions in 11-dimensions corresponding to standard supersymmetric M-brane intersections. It is found that the solutions can be obtained by multiplying the brane and the transverse directions with appropriate powers of two hyperbolic functions of time. This is the S-brane analog of the ``harmonic function rule''. The transverse directions can be hyperbolic, flat or spherical. We also discuss some properties of these solutions.Comment: 12 pages, Latex, a reference adde

Supergravity Solutions for Harmonic, Static and Flux S-Branes

We seek S-brane solutions in D=11 supergravity which can be characterized by a harmonic function H on the flat transverse space. It turns out that the Einstein's equations force H to be a linear function of the transverse coordinates. The codimension one H=0 hyperplane can be spacelike, timelike or null and the spacelike case reduces to the previously obtained SM2 or SM5 brane solutions. We then consider static S-brane configurations having smeared timelike directions where the transverse Lorentzian symmetry group is broken down to its maximal orthogonal subgroup. Assuming that the metric functions depend on a radial spatial coordinate, we construct explicit solutions in D=11 supergravity which are non-supersymmetric and asymptotically flat. Finally, we obtain spacelike fluxbrane backgrounds which have timelike electric or magnetic fluxlines extending from past to future infinity.Comment: 22 pages, v2: references adde

Fermi Liquid Properties of a Two Dimensional Electron System With the Fermi Level Near a van Hove Singularity

We use a diagrammatic approach to study low energy physics of a two dimensional electron system where the Fermi level is near van-Hove singularies in the energy spectrum. We find that in most regions of the $\epsilon_F-T$ phase diagram the system behaves as a normal Fermi liquid rather than a marginal Fermi liquid. Particularly, the imaginary part of the self energy is much smaller than the excitation energy, which implies well defined quasiparticle excitations, and single particle properties are only weakly affected by the presence of the van-Hove singularities. The relevance to high temperature superconductivity is also discussed.Comment: 10 pages, 4 postscript figure

Spectral high resolution feature selection for retrieval of combustion temperature profiles

Proceeding of: 7th International Conference on Intelligent Data Engineering and Automated Learning, IDEAL 2006 (Burgos, Spain, September 20-23, 2006)The use of high spectral resolution measurements to obtain a retrieval of certain physical properties related with the radiative transfer of energy leads a priori to a better accuracy. But this improvement in accuracy is not easy to achieve due to the great amount of data which makes difficult any treatment over it and it's redundancies. To solve this problem, a pick selection based on principal component analysis has been adopted in order to make the mandatory feature selection over the different channels. In this paper, the capability to retrieve the temperature profile in a combustion environment using neural networks jointly with this spectral high resolution feature selection method is studied.Publicad

Special symplectic Lie groups and hypersymplectic Lie groups

A special symplectic Lie group is a triple $(G,\omega,\nabla)$ such that $G$ is a finite-dimensional real Lie group and $\omega$ is a left invariant symplectic form on $G$ which is parallel with respect to a left invariant affine structure $\nabla$. In this paper starting from a special symplectic Lie group we show how to ``deform" the standard Lie group structure on the (co)tangent bundle through the left invariant affine structure $\nabla$ such that the resulting Lie group admits families of left invariant hypersymplectic structures and thus becomes a hypersymplectic Lie group. We consider the affine cotangent extension problem and then introduce notions of post-affine structure and post-left-symmetric algebra which is the underlying algebraic structure of a special symplectic Lie algebra. Furthermore, we give a kind of double extensions of special symplectic Lie groups in terms of post-left-symmetric algebras.Comment: 32 page