Restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry

In this paper, we elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar–tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a nonzero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski spacetime, but the resultant Nambu–Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu–Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu–Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincaré symmetry.

Symmetry Breakdown Related Fracture in 42CrMo4 Steel

Austenite grains that underwent the f.c.c. to b.c.c. (or b.c.t.) transformation are typically composed of 24 Kurdjumov–Sachs variants that can be categorized by three axes of Bain transformations; thus, a complete transformation generally displays 3-fold symmetry in (001) pole figures. In the present work, crystallographic symmetry in 42CrMo4 steel austempered below martensite start temperature was investigated with the help of the orientation distribution function (ODF) analysis based on the FEG-SEM/EBSD technique. It is shown that, upon phase transformations, the specimens contained 6-fold symmetry in all (001), (011), and (111) pole figures of an ODF. The ODF analysis, verified by theoretical modeling, showed that under plane-strain conditions cracks prefer to propagate through areas strongly offset by the high symmetry. The origin of high symmetry was investigated, and the mechanism of the symmetry breakdown was explained.

Pressure Drop Oscillations with Symmetry Breakdown in Two-Phase Flow Parallel Channels

Two-phase flow in parallel heated channels is prone to symmetry breakdown resulting in mass flow maldistribution. Moreover, in the presence of compressible volume, such systems also undergo pressure drop oscillations (PDO). The performances of such systems depend on the effect of these flow instabilities. However, the simultaneous occurrence of these two- phenomena has been rarely reported in the literature. In the present work, an approach is applied in a two channels system to demarcate the parameter space of mass flow rate and inlet temperature into several areas, where these two phenomena take place. The loss in the symmetry in the flow rate is observed as the mass flow rate is varied, which leads to flow maldistribution. The PDO are also observed for specific values of mass flow rate in the system. One unique feature of the parallel channel system is the existence of the oscillatory and stable (albeit asymmetric) states at the same parameter values. For these parameter values, the final state of the system is dependent on the type of initial disturbance. The flow maldistribution due to symmetry breakdown is identified by the pitchfork bifurcation, and oscillations of mass flow rate are identified by the presence of Hopf bifurcation. Moreover, the physical interpretation of the different phenomena in the system is carried out using internal and external pressure drop characteristics curves.

Higgs potential from Weyl conformal gravity

We consider Weyl’s conformal gravity coupled to a complex matter field in Weyl geometry. It is shown that a Higgs potential naturally arises from a [Formula: see text] term in moving from the Jordan frame to the Einstein frame. A massless Nambu–Goldstone boson, which stems from spontaneous symmetry breakdown of the Weyl gauge invariance, is absorbed into the Weyl gauge field, thereby the gauge field becoming massive. We present a model where the gravitational interaction generates a Higgs potential whose form is a perfect square. Finally, we show that a theory in the Jordan frame is gauge-equivalent to the corresponding theory in the Einstein frame via the BRST formalism.

Dp-brane Dynamics and Thermalization in Type IIB Ben Ami-Kuperstein-Sonnenschein Models

We extend and complete our analysis arXiv:1608.02380 and study the induced world volume metrics and Hawking temperatures of all type IIB rotating probe Dp-branes, dual to the temperature of different flavors at finite R-charge, in the Ben Ami–Kuperstein–Sonnenschein holographic models including the effects of spontaneous conformal and chiral flavor symmetry breakdown. The model embeds type IIB probe flavor Dp-branes into the Klebanov-Witten gravity dual of conformal gauge theory, with the embedding parameter, given by the minimal radial extension of the probes, dual to the IR scale of conformal and chiral flavor symmetry breakdown. We show that when the minimal extension is positive definite, the induced world volume metrics of type IIB rotating probe branes admit thermal horizons and Hawking temperatures despite the absence of black holes in the bulk subject to the world volume and topology of the nontrivial internal cycle wrapped by the probe. We also derive the energy–stress tensor of the thermal probes and study their backreaction and energy dissipation. We show that at the IR scale the backreaction is nonnegligible and find the energy can flow from the probes to the bulk, dual to the energy dissipation from the flavor sectors into the gauge theory.