IS GRAVITINO CONDENSATION POSSIBLE?

2004 ◽  
Vol 13 (05) ◽  
pp. 923-933 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Vacuum Energy ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Internal Space ◽  
Superstring Theory ◽  
Spontaneous Compactification ◽  
Expectation Value ◽  
Hidden Sector ◽  
Kähler Potential ◽  
Dimensionless Combination

The condensation of fermion bilinears in the dimensionally-reduced, E 8× E '8 heterotic superstring theory often refers to the E'8 hidden-sector gauginos, but in principle condensation may also occur in the compactified internal space, for example of the gravitino and the spin-1/2 Majorana–Weyl field λ of eleven-dimensional supergravity. This possibility, raised by Duff and Orzalesi as a method of spontaneous compactification that maintains vanishing vacuum energy (cosmological constant), was subsequently considered in the context of the heterotic superstring theory by Helayël–Neto and Smith and by the present author, assuming the internal-space gravitinos [Formula: see text] to condense close to the compactification scale M c ~M P /10. Here, by including the four-fermion terms in the Lagrangian density ℒ, we point out that the observable-sector gravitinos ψi and gauginos g typically have comparable, but not identical, masses m3/2~mg~M c as a result of this process. Hence, such condensation is only permitted either at the much lower scale [Formula: see text] (as for the hidden-sector gaugino condensation), so that [Formula: see text], the upper limit on mg ensuring that the Higgs doublets are sufficiently light or, more plausibly, by setting 1 TeV ~mg≪m3/2~M c , which requires a constraint on the condensate parameters. If the three-index field [Formula: see text] also condenses, then the vacuum expectation value of the dimensionless combination [Formula: see text] of the dilaton A r and modulus B r is fixed at a scale ~1, thus yielding the Kähler potential K and hence m3/2~M c Since B r is determined from supersymmetry, this mechanism determines A r .

scholarly journals COSMOLOGICAL CONCORDANCE MODEL WITH PARTICLE CREATION

2012 ◽  
Vol 18 ◽  
pp. 38-47
Author(s):  
SAULO CARNEIRO
Keyword(s):  
Vacuum Energy ◽  
Particle Creation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
High Energy ◽  
Vacuum Energy Density ◽  
Late Time ◽  
Energy Limit ◽  
Scale Invariant ◽  
Expectation Value

The creation of ultra-light dark particles in the late-time FLRW spacetime provides a cosmological model in accordance with precise observational tests. The matter creation backreaction implies in this context a vacuum energy density scaling linearly with the Hubble parameter H, which is consistent with the vacuum expectation value of the QCD condensate in a low-energy expanding spacetime. Both the cosmological constant and coincidence problems are alleviated in this scenario. We also explore the opposite, high energy limit of the particle creation process. We show that it leads to a non-singular primordial universe where an early inflationary era takes place, with natural reheating and exit. The generated primordial spectrum is scale invariant and, by supposing that inflation lasts for 60 e-folds, we obtain a scalar expectral index n ≈ 0.97.

DARK-MATTER PARTICLES AND BARYONS FROM INFLATION AND SPONTANEOUS CP VIOLATION IN THE EARLY UNIVERSE

2006 ◽  
Vol 21 (15) ◽  
pp. 1183-1188 ◽  
Author(s):  
SAUL BARSHAY ◽  
GEORG KREYERHOFF
Keyword(s):  
Dark Matter ◽  
Early Universe ◽  
Cold Dark Matter ◽  
Vacuum Energy ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Baryon Asymmetry ◽  
Vacuum Energy Density ◽  
Expectation Value ◽  
Residual Vacuum

We present aspects of a model which attempts to unify the creation of cold dark matter, a CP-violating baryon asymmetry, and also a small, residual vacuum energy density, in the early universe. The model contains a primary scalar (inflaton) field and a primary pseudoscalar field, which are initially related by a cosmological, chiral symmetry. The nonzero vacuum expectation value of the pseudoscalar field spontaneously breaks CP invariance.

Global symmetries and Noether’s theorem

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Global Symmetries ◽  
Symmetry Transformation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Quantum Field ◽  
Expectation Value ◽  
Minkowski Space Time ◽  
Integral Measure ◽  
Colour Charge ◽  
Internal Symmetries

Noethers theorem shows that continuous global symmetries lead classically to conservation laws. Such symmetries can be divided into spacetime and internal symmetries. The invariance of Minkowski space-time under global Poincaré transformations leads to the conservation of the four-momentum and the total angular momentum. Examples for conserved charges due to internal symmetries are electric and colour charge. The vacuum expectation value of a Noether current is shown to beconserved in a quantum field theory if the symmetry transformation keeps the path-integral measure invariant.

scholarly journals THE TACHYON FIELD BELOW THE MASS BARRIER

1994 ◽  
Vol 09 (20) ◽  
pp. 3497-3502 ◽  
Author(s):  
D.G. BARCI ◽  
C.G. BOLLINI ◽  
M.C. ROCCA
Keyword(s):  
Green Function ◽  
Eigenvalue Problem ◽  
Plane Wave ◽  
Time Evolution ◽  
Mass Parameter ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Tachyon Field ◽  
Expectation Value ◽  
Wave Solutions

We consider a tachyon field whose Fourier components correspond to spatial momenta with modulus smaller than the mass parameter. The plane wave solutions have then a time evolution which is a real exponential. The field is quantized and the solution of the eigenvalue problem for the Hamiltonian leads to the evaluation of the vacuum expectation value of products of field operators. The propagator turns out to be half-advanced and half-retarded. This completes the proof4 that the total propagator is the Wheeler Green function.4,7

THE TWISTED EUCLIDEAN GREEN’S FUNCTION IN THE SPACETIME OF A COSMIC STRING

1992 ◽  
Vol 01 (02) ◽  
pp. 371-377 ◽  
Author(s):  
B. LINET
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Minkowski Spacetime ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Massive Scalar ◽  
Elementary Functions ◽  
Integral Expression ◽  
Massive Scalar Field ◽  
Expectation Value

In a conical spacetime, we determine the twisted Euclidean Green’s function for a massive scalar field. In particular, we give a convenient form for studying the vacuum averages. We then derive an integral expression of the vacuum expectation value <Φ2(x)>. In the Minkowski spacetime, we express <Φ2(x)> in terms of elementary functions.

Functional Solution Scheme for Relativistic Strong Coupling Theor

1964 ◽  
Vol 19 (7-8) ◽  
pp. 828-834
Author(s):  
G. Heber ◽  
H. J. Kaiser
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Functional Integral ◽  
The Self ◽  
Matrix Elements ◽  
Point Function ◽  
Expectation Value ◽  
Lattice Space ◽  
S Matrix ◽  
Functional Solution

The vacuum expectation value of the S-matrix is represented, following HORI, as a functional integral and separated according to Svac=exp( — i W) ∫ D φ exp( —i ∫ dx Lw). Now, the functional integral involves only the part Lw of the Lagrangian without derivatives and can be easily calculated in lattice space. We propose a graphical scheme which formalizes the action of the operator W = f dx dy δ (x—y) (δ/δ(y))⬜x(δ/δ(x)) . The scheme is worked out in some detail for the calculation of the two-point-function of neutral BOSE fields with the self-interaction λ φM for even M. A method is proposed which under certain convergence assumptions should yield in a finite number of steps the lowest mass eigenvalues and the related matrix elements. The method exhibits characteristic differences between renormalizable and nonrenormalizable theories.

scholarly journals OPERATOR-PRODUCT EXPANSION AND ANALYTICITY

1999 ◽  
Vol 14 (30) ◽  
pp. 4819-4840
Author(s):  
JAN FISCHER ◽  
IVO VRKOČ
Keyword(s):  
Operator Product Expansion ◽  
Deflection Angle ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Operator Product ◽  
Coupling Constant ◽  
Expectation Value ◽  
Euclidean Region ◽  
The Deflection Angle ◽  
Class Of Functions

We discuss the current use of the operator-product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the Euclidean region, we observe how the bound varies with increasing deflection from the Euclidean ray down to the cut (Minkowski region). We argue that the assumption that the remainder is constant for all angles in the cut complex plane down to the Minkowski region is not justified. Making specific assumptions on the properties of the expanded function, we obtain bounds on the remainder in explicit form and show that they are very sensitive both to the deflection angle and to the class of functions considered. The results obtained are discussed in connection with calculations of the coupling constant αs from the τ decay.

THE AFFINE N = 4 YANG–MILLS THEORY

1992 ◽  
Vol 07 (11) ◽  
pp. 2469-2485
Author(s):  
A. C. CADAVID ◽  
R. J. FINKELSTEIN
Keyword(s):  
Mass Spectrum ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Effective Theory ◽  
Affine Algebra ◽  
Linear Mass ◽  
Expectation Value ◽  
Yang Mills ◽  
Exotic States ◽  
Affine Symmetry

An affine field theory may be constructed by gauging an affine algebra. The momentum integrals of the affine N = 4 Yang–Mills theory are ultraviolet finite but diverge because the sum over states is infinite. If the affine symmetry is broken by postulating a nonvanishing vacuum expectation value for that component of the scalar field lying in the L0 direction, then the theory acquires a linear mass spectrum. This broken theory is ultraviolet finite too, but the mass spectrum is unbounded. If it is also postulated that the mass spectrum has an upper bound (say, the Planck mass), then the resulting theory appears to be altogether finite. The influence of the exotic states has been estimated and, according to the proposed scenario, is negligible below energies at which gravitational interactions become important. The final effective theory has the symmetry of a compact Lie algebra augmented by the operator L0.

scholarly journals Weak scale from Planck scale: Mass scale generation in a classically conformal two-scalar system

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Junichi Haruna ◽  
Hikaru Kawai
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Planck Scale ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
The Other ◽  
Expectation Value ◽  
Weak Scale ◽  
The Standard Model ◽  
The One

Abstract In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself cannot explain the origin of the weak scale. On the other hand, from the results of recent accelerator experiments, except for some small corrections, the standard model has increased the possibility of being an effective theory up to the Planck scale. From these facts, it is naturally inferred that the weak scale is determined by some dynamics from the Planck scale. In order to answer this question, we rely on the multiple point criticality principle as a clue and consider the classically conformal $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant two-scalar model as a minimal model in which the weak scale is generated dynamically from the Planck scale. This model contains only two real scalar fields and does not contain any fermions or gauge fields. In this model, due to a Coleman–Weinberg-like mechanism, the one-scalar field spontaneously breaks the $ \mathbb{Z}_2$ symmetry with a vacuum expectation value connected with the cutoff momentum. We investigate this using the one-loop effective potential, renormalization group and large-$N$ limit. We also investigate whether it is possible to reproduce the mass term and vacuum expectation value of the Higgs field by coupling this model with the standard model in the Higgs portal framework. In this case, the one-scalar field that does not break $\mathbb{Z}_2$ can be a candidate for dark matter and have a mass of about several TeV in appropriate parameters. On the other hand, the other scalar field breaks $\mathbb{Z}_2$ and has a mass of several tens of GeV. These results will be verifiable in near-future experiments.

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