DIMENSIONAL REDUCTION AND THE VACUUM STATE IN THE SUPERSTRING THEORY

2002 ◽  
Vol 17 (30) ◽  
pp. 1965-1972 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Effective Action ◽  
Dimensional Reduction ◽  
Euler Number ◽  
Physical Space ◽  
Vacuum State ◽  
Number Density ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Derivative Term

The ten-dimensional effective action of the heterotic superstring theory contains a quadratic higher-derivative term in the form of the Euler-number density [Formula: see text]. We discuss the role of this term in determining the dimensionality [Formula: see text] of the physical space–time, obtained by dimensional reduction, applying the Feynman propagator and the zero-action hypothesis.

ON THE DERIVATION OF THE WHEELER-DEWITT EQUATION IN THE HETEROTIC SUPERSTRING THEORY

1992 ◽  
Vol 07 (17) ◽  
pp. 4149-4165 ◽  
Author(s):  
M.D. POLLOCK
Keyword(s):  
Quantum Mechanics ◽  
Euler Number ◽  
Number Density ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Effective Lagrangian ◽  
Total Divergence ◽  
Set Up ◽  
The Universe ◽  
Non Locality

It has been shown by Pollock that the Wheeler-DeWitt equation for the wave function of the Universe Ψ cannot be derived for the D-dimensional, heterotic superstring theory, when higher-derivative terms [Formula: see text] are included in the effective Lagrangian [Formula: see text], because they occur as the Euler-number density [Formula: see text]. This means that [Formula: see text] cannot be written in the standard Hamiltonian form, and hence that macroscopic quantum mechanics does not exist at this level of approximation. It was further conjectured that the solution to this difficulty is to take into account the effect of the terms [Formula: see text], an expression for which has been obtained by Gross and Witten, and by Freeman et al. Here, this conjecture is proved, but it is pointed out that the theory must first be reduced to a lower dimensionality [Formula: see text]. When this is done, the reduced term R2 is no longer proportional to [Formula: see text], because of additional contributions arising from the dimensional reduction of [Formula: see text]. The Wheeler-DeWitt equation can now be derived in the form of a Schrödinger equation, in particular when [Formula: see text] (and [Formula: see text] is a total divergence which can be discarded), and quantum mechanics can be set up in the usual way. In the light of these results, it is argued that the non-locality of quantum mechanics is related to the cosmological horizon problem.

ON THE SUPERSTRING HAMILTONIAN IN THE FRIEDMANN SPACE–TIME

2006 ◽  
Vol 15 (06) ◽  
pp. 845-868 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Cosmological Solution ◽  
Vacuum State ◽  
Einstein Condensate ◽  
De Sitter ◽  
Superstring Theory ◽  
Bose Einstein Condensate ◽  
Higher Derivative ◽  
Effective Lagrangian ◽  
State Formula ◽  
De Sitter Vacuum

The ten-dimensional effective Lagrangian [Formula: see text] for the gravitational sector of the heterotic superstring theory is known up to quartic higher-derivative order [Formula: see text]. In cosmology, the reduced, four-dimensional line element assumes the Friedmann form ds2 = dt2 - a(t)2dx2, where t is comoving time and a(t) ≡ a0eα(t) is the radius function of the three-space dx2, whose curvature is k = 0, ± 1. The four-Lagrangian can then be expressed as the power-series [Formula: see text], where ˙ ≡ d/dt, from which the field equation can be derived by the method of Ostrogradsky. Here, we determine the coefficients Λ0, An, Bn, Cn, and Kn, which are all non-vanishing in general. We recover the previously obtained, high-curvature, anti-de Sitter vacuum state [Formula: see text] with effective cosmological constant Λ = {18/[175ζ(3) - 1/2]}1/3A r κ-2, whose existence makes it possible to envisage a singularity-free and horizon-free cosmological solution, stable to linear perturbations. It is interesting that all the coefficients of quartic origin arise from the near-cancellation of sums of opposite sign but magnitude f ≈ (28.6–369) times larger than the answer. They thus exhibit a slight asymmetry with regard to positive and negative energies, the anti-de Sitter vacuum being characterized by positive Nordström energy, and therefore only accessible at high curvatures. This vacuum state is a Bose–Einstein condensate of non-interacting gravitons at zero temperature, which, referred to comoving time, can only be formulated after the Wick rotation t → ±iτ, resulting in an imaginary horizon.

INFLATION FROM THE SUPERSTRING VACUUM

2009 ◽  
Vol 24 (20n21) ◽  
pp. 4021-4037
Author(s):  
M. D. POLLOCK
Keyword(s):  
Background Radiation ◽  
Physical Space ◽  
Reduction Process ◽  
Tree Level ◽  
Internal Space ◽  
De Sitter ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Effective Lagrangian ◽  
Microwave Background Radiation

Quartic higher-derivative gravitational terms in the effective Lagrangian of the heterotic superstring theory renormalize the bare, four-dimensional gravitational coupling [Formula: see text], due to the reduction process [Formula: see text], according to the formula [Formula: see text], where A r and B r are the moduli for the physical space gij(xk) and internal space [Formula: see text], respectively. The Euler characteristic [Formula: see text] is negative for a three-generation Calabi–Yau manifold, and therefore both the additional terms, of tree-level and one-loop origin, produce a decrease in κ-2, which changes sign when κ-2 = 0. The corresponding tree-level critical point is [Formula: see text], if we set [Formula: see text] and λ = 15π2, for compactification onto a torus. Values [Formula: see text] yield the anti-gravity region κ-2 < 0, which is analytically accessible from the normal gravity region κ-2 > 0. The only non-singular, vacuum minimum of the potential [Formula: see text] is located at the point [Formula: see text], where [Formula: see text], the quadratic trace anomaly [Formula: see text] dominates over [Formula: see text], and a phase of de Sitter expansion may occur, as first envisaged by Starobinsky, in approximate agreement with the constraint due to the effect of gravitational waves upon the anisotropy of the cosmic microwave background radiation. There is no non-singular minimum of the potential [Formula: see text].

RENORMALIZATION EFFECTS IN THE SUPERSTRING MODULI FROM THE HIGHER-DERIVATIVE TERMS

2001 ◽  
Vol 16 (19) ◽  
pp. 3217-3235 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Equation Of State ◽  
Kinetic Energy ◽  
Canonical Form ◽  
Dimensional Reduction ◽  
Scalar Fields ◽  
Adiabatic Index ◽  
Einstein Metric ◽  
Tree Level ◽  
Superstring Theory ◽  
Higher Derivative

The dimensional reduction of the effective ten-action [Formula: see text] of the heterotic superstring theory to the physical four-action S[gij] results in the appearance of three moduli B(a), whose real parts [Formula: see text], set equal for simplicity, define the radius and shape of the compact internal six-space [Formula: see text], in addition to the dilaton [Formula: see text], the ten-interval being [Formula: see text]. These scalar fields are massless at tree level and can be put into canonical form with coefficients [Formula: see text] for the positive kinetic-energy terms, when higher-derivative terms are ignored, as found by Witten, so that [Formula: see text]. Previously, we have shown that σA and σB acquire a potential from the higher-derivative terms [Formula: see text] and [Formula: see text], which becomes large close to the Planck era. Here, we discuss the renormalization of the kinetic-energy terms due to [Formula: see text] which, after diagonalization, results in a mixing of ∇σB with ∇σA, while the remaining coefficient of (∇σB)2 vanishes at t c ≈ t P /12 in a radiation-dominated Universe, corresponding to a temperature T c ≈ 5 × 1017 GeV , where the four-theory is still classical. At earlier times, the energy is unbounded from below, signalling that the four-theory has become unphysical, and that the string must still be in its uncompactified form with one dilaton ϕ, whose canonical kinetic energy is positive in the Einstein metric. This mechanism depends upon the equation of state of the source for the Friedmann expansion assumed, and is only effective for values of the adiabatic index in the range 1.14 < γ < 2.63, which thus includes radiation (γ = 4/3) and the Zel'dovich equation of state (γ = 2).

DIMENSIONAL REDUCTION AND THE DUALITY SYMMETRY IN THE SUPERSTRING THEORY

1992 ◽  
Vol 07 (08) ◽  
pp. 1833-1849 ◽  
Author(s):  
M.D. POLLOCK
Keyword(s):  
Dimensional Reduction ◽  
Unit Length ◽  
Physical Space ◽  
Space Time ◽  
Density Fluctuations ◽  
Internal Space ◽  
Type I ◽  
Superstring Theory ◽  
Negative Dimension ◽  
Duality Symmetry

The D-dimensional superstring theory is known to be invariant under the duality symmetry b ↔ α'/b, where [Formula: see text] is the constant radius of the N-dimensional internal space and α′ is the slope parameter, the (M+1)-dimensional physical space-time being flat, where D= M+N+1. It is shown, starting from the D-dimensional, vacuum Einstein theory, that this symmetry can be generalized to a curved space-time, with β(t)=–α(t) and [Formula: see text], where t is comoving time, but it will only be an isometry of the (conformally transformed) physical space if this is characterized by a single radius function eα(t). This would explain the homogeneity, isotropy and flatness of the Universe. The dimensionalities are uniquely determined by the dimensional reduction to be D=10, M=3, N=6. Further aspects of the duality symmetry are discussed and the notion of a negative dimension is introduced. For the closed type I superstring, density fluctuations sufficient to account for the presence of galaxies will be present, provided that Gμ≲10−6, where [Formula: see text] is the Newtonian gravitational constant, MP is the Planck mass and μ=α′2/2πb6 is the effective mass per unit length of the string. This condition agrees with the estimate [Formula: see text], obtained by Klein via quantization of the electric charge in the Kaluza-Klein theory. It is also in accord with the expectation that all the higher-dimensional superstring scales are of approximately the same order of magnitude.

scholarly journals Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
B. S. Merzlikin ◽  
K. V. Stepanyantz
Keyword(s):  
Effective Action ◽  
A Priori ◽  
Coupling Constant ◽  
Harmonic Superspace ◽  
Classical Action ◽  
Higher Derivative ◽  
Component Approach ◽  
Dimensionless Coupling ◽  
The One ◽  
Dimensionless Coupling Constant

Abstract We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and $$ \mathcal{N} $$ N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

The “Tracing and Mailing Services” in aid of the “Boat People”

1987 ◽  
Vol 27 (257) ◽  
pp. 203-207
Author(s):  
Pierre Ryter
Keyword(s):  
Effective Action ◽  
Red Cross ◽  
International Network ◽  
International Conference ◽  
Boat People

In Resolution XVI (The role of the Central Tracing Agency and National Societies in tracing activities and the reuniting of families), the Twenty-fifth International Conference of the Red Cross (Geneva, October 1986)… “recalling the role which the Central Tracing Agency (CTA) of the ICRC plays as a co-ordinator and technical adviser to National Societies and governments, as defined in the report presented by the ICRC and the League and adopted by the Twenty-fourth International Conference of the Red Cross,”… and “recognizing that, in order to take effective action, the Movement must be able to rely on a sound network composed of all the National Societies' tracing services and the CTA, in liaison, when necessary, with the League Secretariat,”… encouraged the CTA “to continue its efforts to co-ordinate activities, to harmonize operating principles and working methods, and to train responsible tracing personnel,” and requested “all National Societies to carry out to the best of their capacity the role which they are called upon to play as components of the international network for tracing and reuniting families”.

scholarly journals FROM p-BRANES TO COSMOLOGY

1999 ◽  
Vol 14 (26) ◽  
pp. 4121-4142 ◽  
Author(s):  
H. LÜ ◽  
S. MUKHERJI ◽  
C. N. POPE
Keyword(s):  
String Theory ◽  
Effective Action ◽  
Dimensional Reduction ◽  
Cosmological Models ◽  
Cosmological Solutions ◽  
M Theory ◽  
The Relationship

We study the relationship between static p-brane solitons and cosmological solutions of string theory or M theory. We discuss two different ways in which extremal p-branes can be generalized to nonextremal ones, and show how wide classes of recently discussed cosmological models can be mapped into nonextremal p-brane solutions of one of these two kinds. We also extend previous discussions of cosmological solutions to include some that make use of cosmological-type terms in the effective action that can arise from the generalized dimensional reduction of string theory or M theory.

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