Implications of the Conformal Higgs Model

The postulate of universal local Weyl scaling (conformal) symmetry modifies both general relativity and the Higgs scalar field model. The conformal Higgs model (CHM) acquires a cosmological effect that fits the observed accelerating Hubble expansion for redshifts z≤1 (7.33 Gyr) accurately with only one free constant parameter. Conformal gravity (CG) has recently been fitted to anomalous rotation data for 138 galaxies. Conformal theory explains dark energy and does not require dark matter, providing a viable alternative to the standard ΛCDM paradigm. The theory precludes a massive Higgs particle but validates a composite gauge field W2 with mass 125 GeV.

Conformal Higgs model: Gauge fields can produce a 125 GeV resonance

Recent cosmological observations and compatible theory offer an understanding of long-mysterious dark matter and dark energy. The postulate of universal conformal local Weyl scaling symmetry, without dark matter, modifies action integrals for both Einstein–Hilbert gravitation and the Higgs scalar field by gravitational terms. Conformal theory accounts for both observed excessive external galactic orbital velocities and for accelerating cosmic expansion. SU(2) symmetry-breaking is retained by the conformal scalar field, which does not produce a massive Higgs boson, requiring an alternative explanation of the observed LHC 125 GeV resonance. Conformal theory is shown here to be compatible with a massive neutral particle or resonance [Formula: see text] at 125 GeV, described as binary scalars [Formula: see text] and [Formula: see text] interacting strongly via quark exchange. Decay modes would be consistent with those observed at LHC. Massless scalar field [Formula: see text] is dressed by the [Formula: see text] field to produce Higgs Lagrangian term [Formula: see text] with the empirical value of [Formula: see text] known from astrophysics.

Exact results in a $$ \mathcal{N} $$ = 2 superconformal gauge theory at strong coupling

We consider the $$ \mathcal{N} $$ N = 2 SYM theory with gauge group SU(N) and a matter content consisting of one multiplet in the symmetric and one in the anti-symmetric representation. This conformal theory admits a large-N ’t Hooft expansion and is dual to a particular orientifold of AdS5 × S5. We analyze this gauge theory relying on the matrix model provided by localization à la Pestun. Even though this matrix model has very non-trivial interactions, by exploiting the full Lie algebra approach to the matrix integration, we show that a large class of observables can be expressed in a closed form in terms of an infinite matrix depending on the ’t Hooft coupling λ. These exact expressions can be used to generate the perturbative expansions at high orders in a very efficient way, and also to study analytically the leading behavior at strong coupling. We successfully compare these predictions to a direct Monte Carlo numerical evaluation of the matrix integral and to the Padé resummations derived from very long perturbative series, that turn out to be extremely stable beyond the convergence disk |λ| < π2 of the latter.

Critical behaviour of hydrodynamic series

We investigate the time-dependent perturbations of strongly coupled $$ \mathcal{N} $$ N = 4 SYM theory at finite temperature and finite chemical potential with a second order phase transition. This theory is modelled by a top-down Einstein-Maxwell-dilaton description which is a consistent truncation of the dimensional reduction of type IIB string theory on AdS5×S5. We focus on spin-1 and spin-2 sectors of perturbations and compute the linearized hydrodynamic transport coefficients up to the third order in gradient expansion. We also determine the radius of convergence of the hydrodynamic mode in spin-1 sector and the lowest non-hydrodynamic modes in spin-2 sector. Analytically, we find that all the hydrodynamic quantities have the same critical exponent near the critical point θ = $$ \frac{1}{2} $$ 1 2 . Moreover, we propose a relation between symmetry enhancement of the underlying theory and vanishing of the only third order hydrodynamic transport coefficient θ1, which appears in the shear dispersion relation of a conformal theory on a flat background.

The effective action of superrotation modes

Starting from an analysis of four-dimensional asymptotically flat gravity in first order formulation, we show that superrotation reparametrization modes are governed by an Alekseev-Shatashvili action on the celestial sphere. This two-dimensional conformal theory describes spontaneous symmetry breaking of Virasoro superrotations together with the explicit symmetry breaking of more general Diff($$ {\mathcal{S}}^2 $$ S 2 ) superrotations. We arrive at this result by first reformulating the asymptotic field equations and symmetries of the radiative vacuum sector in terms of a Chern-Simons theory at null infinity, and subsequently performing a Hamiltonian reduction of this theory onto the celestial sphere.

Scale-fixed predictions for γ + ηc production in electron-positron collisions at NNLO in perturbative QCD

In the paper, we present QCD predictions for γ + ηc production at an electron-positron collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for e+ + e− → γ + ηc using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the e+e− center-of-mass collision energy $$ \sqrt{s} $$ s . The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal β contributions into the QCD coupling αs(Q2). The renormalization group equation then sets the value of αs for the process. The PMC renormalization scale reflects the virtuality of the underlying process, and the resulting predictions satisfy all of the requirements of renormalization group invariance, including renormalization scheme invariance. After applying the PMC, we obtain a renormalization scale-and-scheme independent prediction, σ|NNLO,PMC ≃ 41.18 fb for $$ \sqrt{s} $$ s =10.6 GeV. The resulting pQCD series matches the series for conformal theory and thus has no divergent renormalon contributions. The large K factor which contributes to this process reinforces the importance of uncalculated NNNLO and higher-order terms. Using the PMC scale-and-scheme independent conformal series and the Padé approximation approach, we predict σ|NNNLO,PMC+Pade ≃ 18.99 fb, which is consistent with the recent BELLE measurement $$ {\sigma}^{\mathrm{obs}}={16.58}_{-9.93}^{+10.51} $$ σ obs = 16.58 − 9.93 + 10.51 fb at $$ \sqrt{s} $$ s ≃ 10.6 GeV. This procedure also provides a first estimate of the NNNLO contribution.

Line and surface defects for the free scalar field

For a single free scalar field in d ≥ 2 dimensions, almost all the unitary conformal defects must be ‘trivial’ in the sense that they cannot hold interesting dynamics. The only possible exceptions are monodromy defects in d ≥ 4 and co-dimension three defects in d ≥ 5. As an intermediate result we show that the n-point correlation functions of a conformal theory with a generalized free spectrum must be those of the generalized free theory.

4-point function from conformally coupled scalar in AdS6

We explore conformally coupled scalar theory in AdS6 extensively and their classical solutions by employing power expansion order by order in its self-interaction coupling λ. We describe how we get the classical solutions by diagrammatic ways which show general rules constructing the classical solutions. We study holographic correlation functions of scalar operator deformations to a certain 5-dimensional conformal field theory where the operators share the same scaling dimension ∆ = 3, from the classical solutions. We do not assume any specific form of the micro Lagrangian density of the 5-dimensional conformal field theory. For our solutions, we choose a scheme where we remove co-linear divergences of momenta along the AdS boundary directions which frequently appear in the classical solutions. This shows clearly that the holographic correlation functions are free from the co-linear divergences. It turns out that this theory provides correct conformal 2- and 3- point functions of the ∆ = 3 scalar operators as expected in previous literature. It makes sense since 2- and 3- point functions are determined by global conformal symmetry not being dependent on the details of the conformal theory. We also get 4-point function from this holographic model. In fact, it turns out that the 4-point correlation function is not conformal because it does not satisfy the special conformal Ward identity although it does dilation Ward identity and respect SO(5) rotation symmetry. However, in the co-linear limit that all the external momenta are in a same direction, the 4-point function is conformal which means that it satisfy the special conformal Ward identity. We inspect holographic n-point functions of this theory which can be obtained by employing a certain Feynman-like rule. This rule is a construction of n-point function by connecting l-point functions each other where l < n. In the co-linear limit, these n-point functions reproduce the conformal n-point functions of ∆ = 3 scalar operators in d = 5 Euclidean space addressed in arXiv:2001.05379.

Shape analysis via inconsistent surface registration

In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometr- ics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid surface mapping methods rely on a strong assumption of the global consistency of two surfaces. From a practical point of view, given two anatomical surfaces with prominent feature landmarks, it is more desirable to have a method that automatically detects the most relevant parts of the two surfaces and finds the optimal landmark-matching alignment between these parts, without assuming any global 1–1 correspondence between the two surfaces. Our method is capable of solving this problem using inconsistent surface registration based on quasi-conformal theory. It further enables us to quantify the dissimilarity of two shapes using quasi-conformal distortion and differences in mean and Gaussian curvatures, thereby providing a natural way for shape classification. Experiments on Platyrrhine molars demonstrate the effectiveness of our method and shed light on the interplay between function and shape in nature.