GOLDSTONE FIELDS IN THE SUPERSTRING THEORY

2008 ◽  
Vol 17 (01) ◽  
pp. 81-94 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Cosmological Constant ◽  
Goldstone Boson ◽  
Gauge Coupling ◽  
Einstein Equations ◽  
Level Gauge ◽  
Tree Level ◽  
Internal Space ◽  
Spin Component ◽  
Additional Contribution ◽  
Superstring Theory

If global supersymmetry is broken by gaugino condensation in the hidden sector of the [Formula: see text] heterotic superstring theory after compactification, then the auxiliary field FB of the modulus B ≡ (B r , B i ) attains a finite value, while that of the dilaton A ≡ (A r , A i ) vanishes, FA = 0, the Goldstone fermion being the modulino [Formula: see text], the spin-½ component of the complex chiral supermultiplet [Formula: see text]. The Goldstone boson of the scale symmetry that is broken when the radius of the internal space is fixed at a constant value is B r , which is determined from the goldstino Lagrangian, compared term by term with the superstring Lagrangian, including higher-derivative gravitational terms [Formula: see text] and [Formula: see text], after linking the space–time curvature to the energy–momentum tensor of the goldstino via the Einstein equations. This non-linear formulation of supersymmetry, due to Volkov and Akulov, is expressed in terms of the goldstino alone, whose Lagrangian contains a negative cosmological constant, which can be cancelled by the super-Higgs mechanism of Deser and Zumino to make the gravitino massive and break supersymmetry at the level [Formula: see text] GeV, while [Formula: see text]. Here, the modulus has been scaled to the Hagedorn value for the heterotic superstring theory, [Formula: see text], and A r , identified with the inverse square of the tree-level gauge coupling, has been scaled to the calculation in the minimal supersymmetric standard model due to Weinberg, that g-2 = 1.39 at the unification mass MX = 2.2 × 1016 GeV, assuming three generations of elementary particles and two Higgs doublets. In the presence of gravitino condensation in the internal space, however, there is an arbitrary additional contribution to the cosmological constant, facilitating reduction of m s to ~ 100 TeV, say, and m3/2 to ~ 1 eV.

THE VACUUM STATE IN THE HETEROTIC SUPERSTRING THEORY

2007 ◽  
Vol 16 (04) ◽  
pp. 591-618 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Cosmological Constant ◽  
Functional Dependence ◽  
Gauge Coupling ◽  
Vacuum State ◽  
De Sitter Space ◽  
Small Radius ◽  
Internal Space ◽  
Quadratic Term ◽  
De Sitter ◽  
Superstring Theory

The gravitational vacuum state of the heterotic superstring theory is derived by substituting the maximally symmetric D-space [Formula: see text], where [Formula: see text] is the cosmological constant, into the classical field equations obtained from the effective ten-Lagrangian including quartic higher-derivative terms, [Formula: see text]. If the theory is reduced to the physical dimensionality D = 4, as required by supersymmetry and phenomenology, the ground state, due to [Formula: see text] and [Formula: see text], is anti-de Sitter space with [Formula: see text], where [Formula: see text] is the inverse gauge coupling and κ2 ≡ 8πG N is the gravitational coupling, G N being the Newton constant. The term [Formula: see text], derived from the Euler-number density [Formula: see text], is a total divergence and the quadratic term [Formula: see text], derived from [Formula: see text], vanishes identically, while the quadratic anomaly [Formula: see text], which alone would give rise to a positive Λ(anom), is ignorable for the reduced [Formula: see text] heterotic string, containing n v = 488 vector fields, because Λ( anom ) ≳ -Λ unless n v ≳ 7,000. For hypothetical reduction to the higher dimensonalities D = 5, 9, 10, [Formula: see text] has the effect of augmenting the Boulware–Deser, anti-de Sitter space vacuum due to [Formula: see text], which becomes exact when D = 8, for which [Formula: see text] vanishes identically, but leads to a de Sitter space for D = 6, 7 thus justifying the Ricci-flat vacuum state for the six-dimensional internal space. For simplicity, we assume compactification onto a toroidal internal space when D ≥ 5, so that all contributions of the form [Formula: see text] vanish. The remaining terms [Formula: see text] and [Formula: see text] are then almost comparable in effect, bringing into question the convergence of the Lagrangian power series [Formula: see text] in the Einstein space, and consequently the validity of the results obtained. Without knowledge of the yet higher-order terms [Formula: see text], n ≥ 6, however, no further analysis is possible. As they stand the results constitute a realization of the limiting-curvature hypothesis of Frolov et al., and are also discussed from the viewpoint of causality. Finally, the dimensional parameter a, introduced by Volkov and Akulov to define the non-linear global supersymmetry transformations, gives rise to a negative cosmological constant -κ2/a, which can therefore be identified with Λ (which has the functional dependence [Formula: see text] found by Freedman and Das for extended supergravity). This leads to the estimate B r ~ 2 for the dimensionless radius-squared of the internal space, implying a small radius of compactification, in agreement with previous estimates obtained via supersymmetry, and provides a realization of the super-Higgs effect.

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].

scholarly journals HIGGS MECHANISM WITH A TOPOLOGICAL TERM

2001 ◽  
Vol 16 (23) ◽  
pp. 1493-1503 ◽  
Author(s):  
ICHIRO ODA
Keyword(s):  
Degrees Of Freedom ◽  
Goldstone Boson ◽  
Higgs Mechanism ◽  
Tree Level ◽  
Gauge Fields ◽  
Massless Scalar ◽  
Time Dimension ◽  
Superstring Theory ◽  
Gauge Groups ◽  
Topological Term

In cases of both Abelian and non-Abelian gauge groups, we consider the Higgs mechanism in topologically massive gauge theories in an arbitrary space–time dimension. It is shown that the presence of a topological term makes it possible to shift mass of gauge fields in a nontrivial way compared to the conventional value at the classical tree level. We correct the previous misleading statement with respect to the counting of physical degrees of freedom, where it is shown that gauge fields become massive by "eating" the Nambu–Goldstone boson and a higher-rank tensor field, but a new massless scalar appears in the spectrum so the number of physical degrees of freedom remains unchanged before and after the spontaneous symmetry breakdown. Some related phenomenological implications and applications to superstring theory are briefly commented.

ON THE QUARTIC HIGHER-DERIVATIVE GRAVITATIONAL TERMS IN THE HETEROTIC SUPERSTRING THEORY

2006 ◽  
Vol 21 (02) ◽  
pp. 373-404 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Dimensional Space ◽  
Flat Space ◽  
Momentum Tensor ◽  
Space Time ◽  
Einstein Equations ◽  
Quadratic Term ◽  
Additional Contribution ◽  
Superstring Theory ◽  
Weyl Spinor ◽  
Higher Derivative

The quartic higher-derivative gravitational terms [Formula: see text] in the heterotic-superstring effective Lagrangian [Formula: see text], defined from the Riemann ten-tensor [Formula: see text], are expanded, after reduction to the conformally-flat physical D-space gij, in terms of the Ricci tensor Rij and scalar R. The resulting quadratic term [Formula: see text] is tachyon-free and agrees exactly with the prediction from global supersymmetry in the nonlinear realization of Volkov and Akulov of the flat-space, quadratic fermionic Lagrangian [Formula: see text] for a massless Dirac or Weyl spinor, only when D = 4, assuming the Einstein equation [Formula: see text] for the energy–momentum tensor. This proves that the heterotic superstring has to be reduced from ten to four dimensions if supersymmetry is to be correctly incorporated into the theory, and it rules out the bosonic string and type-II superstring, for which [Formula: see text] has the different a priori forms ±(R2-4RijRij) derived from [Formula: see text], which also contain tachyons (that seem to remain after the inclusion of a further contribution to [Formula: see text] from [Formula: see text]). The curvature of space–time introduces a mass into the Dirac equation, [Formula: see text], while quadratic, higher-derivative terms [Formula: see text] make an additional contribution to the Einstein equations, these two effects causing a difference between [Formula: see text] and [Formula: see text] on the one hand, and the predictions from [Formula: see text] and [Formula: see text] on the other. The quartic terms [Formula: see text] still possess some residual symmetry, however, enabling us to estimate the radius-squared of the internal six-dimensional space [Formula: see text] in units of the Regge slope-parameter α′ as B r ≈ 1.75, indicating that compactification occurs essentially at the Planck era, due to quantum mechanical processes, when the action evaluated within the causal horizon is S h ~ 1. This symmetry is also discussed with regard to the zero-action hypothesis. The dimensionality D = 4 of space–time is rederived from the Wheeler–DeWitt equation (Schrödinger equation) of quantum cosmology in the mini-superspace approximation, by demanding invariance and positive-semi-definiteness of the potential [Formula: see text] under Wick rotation of the time coordinate, which also determines the three-space to be flat, so that K = 0, and again involves the nonlinearity of gravitation.

scholarly journals Soft photon theorem in the small negative cosmological constant limit

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Nabamita Banerjee ◽  
Karan Fernandes ◽  
Arpita Mitra
Keyword(s):  
Cosmological Constant ◽  
Tree Level ◽  
Leading Order ◽  
Asymptotically Flat ◽  
Soft Factor ◽  
Flat Spacetime ◽  
Electromagnetic Interactions ◽  
Flat Spacetimes ◽  
Perturbative Corrections ◽  
Soft Factors

Abstract We study the effect of electromagnetic interactions on the classical soft theorems on an asymptotically AdS background in 4 spacetime dimensions, in the limit of a small cosmological constant or equivalently a large AdS radius l. This identifies 1/l2 perturbative corrections to the known asymptotically flat spacetime leading and subleading soft factors. Our analysis is only valid to leading order in 1/l2. The leading soft factor can be expected to be universal and holds beyond tree level. This allows us to derive a 1/l2 corrected Ward identity, following the known equivalence between large gauge Ward identities and soft theorems in asymptotically flat spacetimes.

scholarly journals Phenomenology of Minimal Unified Tree Level Gauge Mediation at the LHC

2013 ◽  
Vol 2013 (7) ◽  
Author(s):  
Maurizio Monaco ◽  
Maurizio Pierini ◽  
Andrea Romanino ◽  
Martin Spinrath
Keyword(s):  
Level Gauge ◽  
Tree Level ◽  
Gauge Mediation

scholarly journals Vacuum solutions of Einstein equations that depend on one coordinate

2020 ◽  
pp. 10-11
Author(s):  
S. Parnovsky
Keyword(s):  
Exact Solution ◽  
General Theory ◽  
Cosmological Constant ◽  
Gravitational Wave ◽  
Einstein Equations ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Vacuum Metrics ◽  
Vacuum Solutions ◽  
Zero Frequency

In the famous textbook written by Landau and Lifshitz all the vacuum metrics of the general theory of relativity are derived, which depend on one coordinate in the absence of a cosmological constant. Unfortunately, when considering these solutions the authors missed some of the possible solutions discussed in this article. An exact solution is demonstrated, which is absent in the book by Landau and Lifshitz. It describes space-time with a gravitational wave of zero frequency. It is shown that there are no other solutions of this type than listed above and Minkowski’s metrics. The list of vacuum metrics that depend on one coordinate is not complete without solution provided in this paper.

scholarly journals Electroweak corrections in a pseudo Nambu-Goldstone Dark Matter model revisited

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Seraina Glaus ◽  
Margarete Mühlleitner ◽  
Jonas Müller ◽  
Shruti Patel ◽  
Tizian Römer ◽  
...  
Keyword(s):  
Dark Matter ◽  
Cross Section ◽  
Parameter Space ◽  
Goldstone Boson ◽  
Indirect Evidence ◽  
Tree Level ◽  
Dark Matter Candidate ◽  
Nucleon Scattering ◽  
The Cross ◽  
Electroweak Corrections

Abstract Having so far only indirect evidence for the existence of Dark Matter a plethora of experiments aims at direct detection of Dark Matter through the scattering of Dark Matter particles off atomic nuclei. For the correct interpretation and identification of the underlying nature of the Dark Matter constituents higher-order corrections to the cross section of Dark Matter-nucleon scattering are important, in particular in models where the tree-level cross section is negligibly small. In this work we revisit the electroweak corrections to the dark matter-nucleon scattering cross section in a model with a pseudo Nambu-Goldstone boson as the Dark Matter candidate. Two calculations that already exist in the literature, apply different approaches resulting in different final results for the cross section in some regions of the parameter space leading us to redo the calculation and analyse the two approaches to clarify the situation. We furthermore update the experimental constraints and examine the regions of the parameter space where the cross section is above the neutrino floor but which can only be probed in the far future.

scholarly journals Cosmological model favored by the holographic principle

2016 ◽  
Vol 41 ◽  
pp. 1660127
Author(s):  
Irina Dymnikova ◽  
Anna Dobosz ◽  
Bożena Sołtysek
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Space Time ◽  
Holographic Principle ◽  
Einstein Equations ◽  
Energy Tensor ◽  
De Sitter ◽  
Quantum Evaporation ◽  
Stress Energy ◽  
De Sitter Vacua

We present a regular spherically symmetric cosmological model of the Lemaitre class distinguished by the holographic principle as the thermodynamically stable end-point of quantum evaporation of the cosmological horizon. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. Global structure of space-time is the same as for the de Sitter space-time. Cosmological evolution goes from a big initial value of the cosmological constant towards its presently observed value.

WORMHOLE SOLUTIONS IN R1×S1×S2 TOPOLOGICAL SPACE

1992 ◽  
Vol 07 (27) ◽  
pp. 2463-2467 ◽  
Author(s):  
SUBENOY CHAKRABORTY
Keyword(s):  
Scalar Field ◽  
Topological Space ◽  
Cosmological Constant ◽  
Symmetric Tensor ◽  
Einstein Equations ◽  
Second Step ◽  
Anisotropic Space ◽  
First Case ◽  
Frw Metric ◽  
Conformal Scalar Field

Wormhole solutions are discussed for two different physical situations in the background of a homogeneous anisotropic space-time. In the first case, the wormholes are solutions of the Euclidean Einstein equations with a cosmological constant and a two-index anti-symmetric tensor for monopole configuration on a space with three-surface of topology S1×S2. In the second step, conformal scalar field is coupled to gravity and wormhole are considered for both λ=0 and λ>0. These results are analogous to the wormhole solutions for FRW metric.

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