In SU($N$) gauge-Higgs theories, with a single Higgs field in the fundamental representation, there exists in addition to the local gauge symmetry a global SU(2) symmetry, at $N=2$, and a global U(1) symmetry, for $N \ne 2$. We construct a gauge-invariant order parameter for the breaking of these global symmetries in the Higgs sector, and calculate numerically the transition lines, in coupling-constant space, for SU(2) and SU(3) gauge theories with unimodular Higgs fields. The order parameter is non-local, and therefore its non-analyticity does not violate the theorem proved by Osterwalder and Seiler. We then show that there exists a transition, in gauge-Higgs theories, between two types of confinement: ordinary color neutrality in the Higgs region, and a stronger condition, which we have called "separation-of-charge confinement," in the confinement region. We conjecture that the symmetry-breaking transition coincides with the transition between these two physically different types of confinement.
A self-contained method of obtaining effective theories resulting from the spontaneous breakdown of conformal invariance is developed. It allows to demonstrate that the Nambu-Goldstone fields for special conformal transformations always represent non-dynamical degrees of freedom. The standard approach to the same question, which includes the imposition of the inverse Higgs constraints, is shown to follow from the developed technique. This provides an alternative view on the nature of the inverse Higgs constraints for the conformal group.
A spontaneously broken SU(2) theory is the simplest generalization of the Abelian Higgs model, containing three equally massive vector bosons and a single Higgs scalar. A strictly diagrammatic proof is presented of the tree-level unitarity of this model in the unitary gauge, i.e. employing only physical fields. A new Ward-like identity is used to show that the high-energy behaviour of all amplitudes cannot be more than quadratic; the use of generating functions for all off-shell amplitudes then leads to the unitarity proof.
We propose that the Higgs phase of a gauge Higgs theory is the phase of spontaneously broken custodial symmetry, and present a new gauge invariant order parameter for custodial symmetry breaking which is very closely analogous to the Edwards-Anderson order parameter for spin glasses. Custodial symmetry is a global symmetry acting on the Higgs field alone, and we show here that the spin glass transition in gauge Higgs theories, from a QCD-like phase to a Higgs phase of broken custodial symmetry, coincides with the transition between two distinct types of confinement. These are color confinement…
The $SO(11)$ gauge-Higgs grand unification in the Randall-Sundrum warped space is presented. The 4D Higgs field is identified as the zero mode of the fifth dimensional component of the gauge potentials, or as the fluctuation mode of the Aharonov-Bohm phase $θ_H$ along the fifth dimension. Fermions are introduced in the bulk in the spinor and vector representations of $SO(11)$. $SO(11)$ is broken to $SO(4) \times SO(6)$ by the orbifold boundary conditions, which is broken to $SU(2)_L \times U(1)_Y \times SU(3)_C$ by a brane scalar. Evaluating the effective potential $V_{\rm eff} (θ_H)$, we show…
The "Goldstone Exception" II: Absence of a Higgs Fine-Tuning Problem in the Spontaneously Broken Limit of the Gell Mann Levy Linear Sigma Model: O(4) with PCAC and SU(2)_L with PCAC and Standard Model Quarks and Leptons
We study the relationship between the strength of fifth forces and the origin of scale breaking in the Standard Model (SM) of particle physics. We start with a light scalar field that is conformally coupled to a toy SM matter sector through a Weyl rescaling of the metric. After appropriately normalizing the fields, the conformally coupled scalar only interacts directly with the would-be Higgs field through kinetic-mixing and Higgs-portal terms. Thus, for the first time, we describe the equivalence of conformally coupled scalar-tensor modifications of gravity and Higgs-portal theories, and we f…
Spontaneously broken Standard Model (SM) symmetries and the Goldstone theorem protect the Higgs mass and ensure that it has no Higgs Fine Tuning Problem (HFTP)
Higgs-Inflaton Symbiosis, Cosmological Constant Problem and Superacceleration Phase of the Universe in Two Measures Field Theory with Spontaneously Broken Scale Invariance
The Ward identities associated with spontaneously broken symmetries can be saturated by Goldstone bosons. However, when space-time symmetries are broken, the number of Goldstone bosons necessary to non-linearly realize the symmetry can be less than the number of broken generators. The loss of Goldstones may be due to a redundancy or the generation of a gap. This phenomena is called an Inverse Higgs Mechanism (IHM). However, there are cases when a Goldstone boson associated with a broken generator does not appear in the low energy theory despite the lack of the existence of an associated IHM. I…
The Gell-Mann-Levy (GML), Schwinger and Standard Models were previously shown to lack a Brout-Englert-Higgs (BEH) fine-tuning problem due to quadratic divergences, with finite Euclidean cut-off Λ, because of the symmetries obeyed by all O(Λ^2) contributions. We extend those results to finite contributions from certain M_{Heavy}^2>> m_{BEH}^2 particles in SO(2) versions of GML and Schwinger. We demonstrate explicit 1-loop physical naturalness for two SO(2) singlet examples: a heavy real scalar S and a right-handed Type 1 see-saw Majorana neutrino. We prove that for low |q^2| the heavy degrees o…
"Super"-Dilatation Symmetry of the Top-Higgs System
顶-希格斯系统，由顶夸克（LH二重态，RH单线态）和希格斯玻色子动力学项组成，规范场设置为零，具有精确（模总发散）对称性，费米子和希格斯场都以超对称的方式移动和混合。完整的Higgs-Yukawa相互作用和Higgs势，包括额外的1/Λ^2 N JL类相互作用，也具有这种对称性到0（1/Λ^4）直到零算符。因此，相互作用拉格朗日量可以看作是1/^2的幂级数。这种对称性涉及到希格斯四次相互作用与希格斯-汤川相互作用的相互作用，并暗示了在高能尺度Λ=几TeV时，顶-汤川耦合g与希格斯四次耦合λ之间的关系λ= \half g ^2。我们认为这是一种新的物理尺度。顶夸克在对称相中是无质量的，满足南武-戈德斯通定理。由于λ和g的相互作用，电流的费米子位移部分为\propto（1-H^ \dagger H/v ^2），在破缺相中消失。因此，在破缺相中，南武-戈德斯通定理被简单地回避了，顶夸克变重了（它不是戈德斯通）。我们有m_t=m_h，经过辐射修正，原则上可以使希格斯粒子与实验一致。
We show that the Higgs and confinement phases of a gauge Higgs theory, with the Higgs field in the fundamental representation of the gauge group, are distinguished both by a broken or unbroken realization of the global center subgroup of the gauge group, and by the type of confinement in each phase. This is color confinement in the Higgs phase, and a stronger property, which we call "separation-of-charge" confinement, in the confining phase.
We establish a classical analog of the Nambu-Goldstone theorem for spontaneous breaking of spacetime symmetries. It provides a counting rule for independent Nambu-Goldstone fields and states which of them are gapped. We demonstrate that only those symmetry group generators give rise to independent Nambu-Goldstone fields that act non-trivially on a vacuum at the origin of coordinates. Other generators give rise to auxiliary fields that must be excluded from a theory by the means of inverse Higgs constraints. The physical meaning of the inverse Higgs phenomenon and an application of our results …
Using Perelman's approach for geometrical flows in terms of an entropy functional, the Higgs mechanism is studied dynamically along flows defined in the space of parameters and in fields space. The model corresponds to two-dimensional gravity that incorporates torsion as the gradient of a Higgs field, and with the reflection symmetry to be spontaneously broken. The results show a discrete mass spectrum, and the existence of a mass gap between the Unbroken Exact Symmetry and the Spontaneously Broken Symmetry scenarios. In the later scenario, the geometries at the degenerate vacua correspond to …
Higgs Mechanism for New Massive Gravity and Weyl Invariant Extensions of Higher Derivative Theories
New Massive Gravity为2+1维的引力子提供了Fierz-Pauli质量的非线性扩展。在这里，我们构建一个外尔不变的版本，这个理论。当外尔对称性破缺时，引力子会得到类似于希格斯机制的质量。在（反）-de Sitter背景中，对称性可以自发破缺，而在平坦背景中，辐射修正在双圈水平上，以Coleman-Weinberg机制破缺Weyl对称性。我们还构造了其他一些高阶导数模型的Weyl不变扩张，如Gauss-Bonnet理论（在三维中约化为Maxwell理论）和Born-Infeld型引力。
In contrast to internal symmetries, there is no general proof that the coset construction for spontaneously broken spacetime symmetries leads to universal dynamics. One key difference lies in the role of Goldstone bosons, which for spacetime symmetries includes a subset which are inessential for the non-linear realisation and hence can be eliminated. In this paper we address two important issues that arise when eliminating inessential Goldstones. The first concerns the elimination itself, which is often performed by imposing so-called inverse Higgs constraints. Contrary to claims in the litera…
We study the coupled system consisting of a complex matter scalar field, a U(1) gauge field, and a complex Higgs scalar field that causes spontaneously symmetry breaking. We show by numerical calculations that there are spherically symmetric nontopological soliton solutions. Homogeneous balls solutions, all fields take constant values inside the ball and in the vacuum state outside, appear in this system. It is shown that the homogeneous balls have the following properties: charge density of the matter scalar field is screened by counter charge cloud of the Higgs and gauge field everywhere; an…
We review a construction called Non-Perturbative Gauge-Higgs Unification which is a rather rare type of Higgs mechanism that is a pure quantum and bosonic effect. It is constructed on a five-dimensional "orbifold lattice" with SU(2) bulk gauge symmetry and a (spontaneously broken) Abelian-Higgs like theory on the boundaries.
We construct, numerically, stationary and spherically symmetric nontopological soliton solutions in the system composed of a complex scalar field, a U(1) gauge field, and a complex Higgs scalar field that causes spontaneous symmetry braking. It is shown that the charge of the soliton is screened by counter charge everywhere.
