Cotton-Squared Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Relational Theory ◽  
Potential Term ◽  
Conformally Invariant ◽  
Invariant Potential ◽  
Cotton Tensor ◽  
Theory Of Gravity

This chapter analyzes a non-viable theory of gravity based on a Jacobi-type action with a conformally invariant potential term based on the square of the Cotton tensor. This theory has striking similarities with Maxwell’s electromagnetism, of which it represents the generalization to spin 2, but unfortunately it is not dynamically consistent, leaving SD as the only viable spatially conformally invariant relational theory of gravity.

scholarly journals Higgs potential from Wick rotation in conformal BSM

2019 ◽  
Vol 34 (31) ◽  
pp. 1950257
Author(s):  
Ichiro Oda
Keyword(s):  
Standard Model ◽  
Conformal Symmetry ◽  
Planck Scale ◽  
Mass Term ◽  
Conformal Factor ◽  
Higgs Potential ◽  
Wick Rotation ◽  
Potential Term ◽  
Conformally Invariant ◽  
Invariant Potential

It is well known that in order to make the path integral of general relativity converge, one has to perform the Wick rotation over the conformal factor in addition to the more familiar Wick rotation of the time axis to pass to the spacetime with Euclidean signature. In this paper, we will apply this technique to a scalar field in the conformally invariant scalar–tensor gravity with a conformally invariant beyond-standard-model (BSM). It is then shown that a potential term in the conformally invariant potential, which corresponds to the Higgs mass term in the Higgs potential of the Standard Model (SM), can have a negative coefficient. The change of sign of the potential term naturally induces spontaneous symmetry breakdown of the electroweak gauge symmetry after symmetry breaking of conformal symmetry (local scale symmetry) via the Coleman–Weinberg mechanism around the Planck scale. This study might shed light on the fact that the existence of a stable vacuum in quantum gravity is relevant to that in the SM.

scholarly journals f(R) View of Lyttleton-Bondi Cosmological Model in Peres Spacetime

2014 ◽  
Vol 8 ◽  
pp. 23-29
Author(s):  
S.N. Pandey ◽  
Sacheendra Shukla
Keyword(s):  
Cosmological Model ◽  
Gravitational Waves ◽  
Field Equations ◽  
Einstein Theory ◽  
Conformally Invariant ◽  
Theories Of Gravity ◽  
Theory Of Gravity

Over the last few years, among various alternatives to the Einstein theory of gravity, especially f(R) theories of gravity have received more importance due to number of interesting results in cosmology and astrophysics. Pandey [10] gave an f(R) theory of gravity to obtain conformally invariant gravitational waves in which field equations have the form given by (3). In this paper we have investigated Lyttleton Bondi Cosmological model in view of field equations of f(R) theory of gravity for Generalized Peres spacetime and finally a wave like solution is obtained.

scholarly journals A First-Quantized Model for Unparticles and Gauge Theories around Conformal Window

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 471
Author(s):  
Nicolas Boulanger ◽  
Fabien Buisseret ◽  
Guillaume Lhost
Keyword(s):  
Bound States ◽  
Gauge Theories ◽  
Mass Operator ◽  
Conformal Symmetry ◽  
Mass Term ◽  
String Tension ◽  
Coupling Constant ◽  
Scalar Particles ◽  
Conformally Invariant ◽  
Invariant Potential

We first quantize an action proposed by Casalbuoni and Gomis in 2014 that describes two massless relativistic scalar particles interacting via a conformally invariant potential. The spectrum is a continuum of massive states that may be interpreted as unparticles. We then obtain in a similar way the mass operator for a deformed action in which two terms are introduced that break the conformal symmetry: a mass term and an extra position-dependent coupling constant. A simple Ansatz for the latter leads to a mass operator with linear confinement in terms of an effective string tension σ. The quantized model is confining when σ≠0 and its mass spectrum shows Regge trajectories. We propose a tensionless limit in which highly excited confined states reduce to (gapped) unparticles. Moreover, the low-lying confined bound states become massless in the latter limit as a sign of conformal symmetry restoration and the ratio between their masses and σ stays constant. The originality of our approach is that it applies to both confining and conformal phases via an effective interacting model.

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