Spontaneous Gauge Symmetry Breaking Research Articles

A new twist on heterotic string compactifications

A rich pattern of gauge symmetries is found in the moduli space of heterotic string toroidal compactifications, at fixed points of the T-duality transformations. We analyze this pattern for generic tori, and scrutinize in full detail compactifications on a circle, where we find all the maximal gauge symmetry groups and the points where they arise. We present figures of two-dimensional slices of the 17-dimensional moduli space of Wilson lines and circle radii, showing the rich pattern of points and curves of symmetry enhancement. We then study the target space realization of the duality symmetry. Although the global continuous duality symmetries of dimensionally reduced heterotic supergravity are completely broken by the structure constants of the maximally enhanced gauge groups, the low energy effective action can be written in a manifestly duality covariant form using heterotic double field theory. As a byproduct, we show that a unique deformation of the generalized diffeomorphisms accounts for both SO(32) and E8 × E8 heterotic effective field theories, which can thus be considered two different backgrounds of the same double field theory even before compactification. Finally we discuss the spontaneous gauge symmetry breaking and Higgs mechanism that occurs when slightly perturbing the background fields, both from the string and the field theory perspectives.

Higgs mechanism in nonlocal field theories

We study spontaneous gauge symmetry breaking and the Higgs mechanism in nonlocal field theories. Motivated by the level truncated action of string field theory, we consider a class of nonlocal field theories with an exponential factor of the d’Alembertian attached to the kinetic and mass terms. Modifications of this kind are known to make mild the UV behavior of loop diagrams and thus have been studied not only in the context of string theory but also as an alternative approach to quantum gravity. In this paper we argue that such a nonlocal theory potentially includes a ghost mode near the nonlocal scale in the particle spectrum of the symmetry broken phase. This is in sharp contrast to local field theories and would be an obstruction to making a simple nonlocal model a UV complete theory. We then discuss a possible way out by studying nonlocal theories with extra symmetries such as gauge symmetries in higher spacetime dimensions.

Gauge-independent Brout\u2013Englert\u2013Higgs mechanism and Yang\u2013Mills theory with a gauge-invariant gluon mass term

For the Yang–Mills theory coupled to a single scalar field in the fundamental representation of the gauge group, we present a gauge-independent description of the Brout–Englert–Higgs mechanism by which massless gauge bosons acquire their mass. The new description should be compared with the conventional gauge-dependent description relying on the spontaneous gauge symmetry breaking due to a choice of the non-vanishing vacuum expectation value of the scalar field. In this paper we focus our consideration on the fundamental scalar field which extends the previous work done for the Yang–Mills theory with an adjoint scalar field. Moreover, we show that the Yang–Mills theory with a gauge-invariant mass term is obtained from the corresponding gauge-scalar model when the radial degree of freedom (length) of the scalar field is fixed. The result obtained in this paper is regarded as a continuum realization of the Fradkin–Shenker continuity and Osterwalder–Seiler theorem for the complementarity between Higgs regime and Confinement regime which was given in the gauge-invariant framework of the lattice gauge theory. Moreover, we discuss how confinement is investigated through the gauge-independent Brout–Englert–Higgs mechanism by starting with the complementary gauge-scalar model.

Gauged Supergravities and Spontaneous Supersymmetry Breaking from the Double Copy Construction.

Supergravities with gauged R symmetry and Minkowski vacua allow for spontaneous supersymmetry breaking and, as such, provide a framework for building supergravity models of phenomenological relevance. In this Letter, we initiate the study of double copy constructions for these supergravities. We argue that, on general grounds, we expect their scattering amplitudes to be described by a double copy of the type (spontaneously broken gauge theory)⊗ (gauge theory with broken supersymmetry). We present a simple realization in which the resulting supergravity has U(1)_{R} gauge symmetry, spontaneously broken N=2 supersymmetry, and massive gravitini. This is the first instance of a double copy construction of a gauged supergravity and of a theory with spontaneously broken supersymmetry. The construction extends in a straightforward manner to a large family of gauged Yang-Mills-Einstein supergravity theories with or without spontaneous gauge-symmetry breaking.

CPT and Lorentz violation in the electroweak sector

Long ago, Carroll, Field and Jackiw introduced CPT-violation in the photon sector by adding a dimension-3 gauge-invariant term parametrized by a constant four-vector parameter kAF to the usual (Maxwell) Lagrangian, deriving an ultra-tight bound from astrophysical data. Here, we will discuss recent work studying the extension of this term to the full electroweak gauge sector of the Standard Model. In the context of the Standard Model Extension, CPT and Lorentz violation arises from two gauge-invariant terms parametrized by the four vectors k1 and k2. First we will show how upon spontaneous breaking of the electroweak gauge symmetry these two terms yield Lorentz-violating terms for the photon and the W and Z bosons. As it turns out, the resulting modified dispersion relations for the W bosons yield spacelike momentum for one of its propagating modes at sufficiently large energy. This in turn allows for the possibility of Cherenkov-like W-boson emission by high-energy fermions such as protons, provoking their decay. Analysis of ultra-high-energy cosmic ray data allows for bounding the previously unbound parameter k2, and, by combination with the ultra-tight bound on kAF, the parameter k1.

Common origin of 3.55 keV x-ray line and gauge coupling unification with left-right dark matter

We present a minimal left-right dark matter framework that can simultaneously explain the recently observed 3.55 keV x-ray line from several galaxy clusters and gauge coupling unification at high energy scale. Adopting a minimal dark matter strategy, we consider both left and right handed triplet fermionic dark matter candidates which are stable by virtue of a remnant ${\mathcal{Z}}_{2}\ensuremath{\simeq}(\ensuremath{-}1{)}^{B\ensuremath{-}L}$ symmetry arising after the spontaneous symmetry breaking of left-right gauge symmetry to that of the standard model. A scalar bitriplet field is incorporated whose first role is to allow radiative decay of right handed triplet dark matter into the left handed one and a photon with energy 3.55 keV. The other role this bitriplet field at TeV scale plays is to assist in achieving gauge coupling unification at a high energy scale within a nonsupersymmetric $SO(10)$ model while keeping the scale of left-right gauge symmetry around the TeV corner. Apart from solving the neutrino mass problem and giving verifiable new contributions to neutrinoless double beta decay and charged lepton flavor violation, the model with TeV scale gauge bosons can also give rise to interesting collider signatures like diboson excess, dilepton plus two jets excess reported recently in the large hadron collider data.

The standard model gauge symmetry from higher-rank unified groups in grand gauge-Higgs unification models

We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on S1/ℤ2. The spontaneous breaking of unified gauge symmetries is achieved via vacuum expectation values of the extra-dimensional components of gauge fields. We derive one-loop effective potentials for the zero modes of the gauge fields in SU(7), SU(8), SO(10), and E6 models. In each model, the rank of the residual gauge symmetry that respects the boundary condition imposed at the orbifold fixed points is higher than that of the standard model. We verify that the residual symmetry is broken to the standard model gauge symmetry at the global minima of the effective potential for certain sets of bulk fermion fields in each model.

Running non-minimal inflation with stabilized inflaton potential

In the context of the Higgs model involving gauge and Yukawa interactions with the spontaneous gauge symmetry breaking, we consider lambda phi ^4 inflation with non-minimal gravitational coupling, where the Higgs field is identified as the inflaton. Since the inflaton quartic coupling is very small, once quantum corrections through the gauge and Yukawa interactions are taken into account, the inflaton effective potential most likely becomes unstable. In order to avoid this problem, we need to impose stability conditions on the effective inflaton potential, which lead to not only non-trivial relations amongst the particle mass spectrum of the model, but also correlations between the inflationary predictions and the mass spectrum. For concrete discussion, we investigate the minimal B-L extension of the standard model with identification of the B-L Higgs field as the inflaton. The stability conditions for the inflaton effective potential fix the mass ratio amongst the B-L gauge boson, the right-handed neutrinos and the inflaton. This mass ratio also correlates with the inflationary predictions. In other words, if the B-L gauge boson and the right-handed neutrinos are discovered in the future, their observed mass ratio provides constraints on the inflationary predictions.

The Journey Through Time Towards the Discovery of the Higgs Boson - A Review

The Higgs mechanics is very powerful, it furnishes a description of the electroweak theory in the standard Model which has a convincing experimental verification. But although the Higgs mechanism had been applied successfully, the conceptual background is not clear. The Higgs mechanism is often presented as spontaneous breaking of local gauge symmetry. But local gauge symmetry is rooted in redundancy of description, gauge transformation connect states that cannot be physically distinguished. Gauge symmetry is therefore not symmetry of nature, but of our description of nature. The spontaneous breaking of such symmetry cannot be expected to have physical effects since asymmetries are not reflected in the physics. If spontaneous gauge symmetry breaking cannot have physical effects, this causes conceptual problems for the Higgs mechanism, if taken to be described as spontaneous gauge symmetry breaking. In a gauge invariant theory, gauge fixing is necessary to retrieve the physics from the theory. This means that also in a theory with spontaneous gauge symmetry breaking, a gauge should be fixed. But gauge fixing itself breaks the gauge symmetry, and thereby obscures the spontaneous breaking of the symmetry. It suggests that spontaneous gauge symmetry breaking is not part of the physics, but an unphysical artefact of the redundancy in description.

The ATLAS diboson resonance in non-supersymmetric SO(10)

SO(10) grand unification accommodates intermediate gauge symmetries with which gauge coupling unification can be realized without supersymmetry. In this paper, we discuss the possibility that a new massive gauge boson associated with an intermediate gauge symmetry explains the excess observed in the diboson resonance search recently reported by the ATLAS experiment. The model we find has two intermediate symmetries, $SU(4)_C \otimes SU(2)_L \otimes SU(2)_R$ and $SU(3)_C \otimes SU(2)_L \otimes SU(2)_R \otimes U(1)_{B-L}$, where the latter gauge group is broken at the TeV scale. This model achieves gauge coupling unification with a unification scale sufficiently high to avoid proton decay. In addition, this model provides a good dark matter candidates, whose stability is guaranteed by a $Z_2$ symmetry present after the spontaneous breaking of the intermediate gauge symmetries. We also discuss prospects for testing these models in the forthcoming LHC experiments and dark matter detection experiments.

Electroweak Symmetry Breaking and the Higgs Boson

The first LHC run has confirmed the Standard Model as the correct theory at the electroweak scale, and the existence of a Higgs-like particle associated with the spontaneous breaking of the electroweak gauge symmetry. These lectures overview the present knowledge on the Higgs boson and discuss alternative scenarios of electroweak symmetry breaking which are already being constrained by the experimental data.

Revolving D-branes and spontaneous gauge-symmetry breaking

We propose a new mechanism of spontaneous gauge symmetry breaking in the world-volume theory of revolving D-branes around a fixed point of orbifolds. In this paper, we consider a simple model of the T6/Z3 orbifold on which we put D3-branes, D7-branes and their anti-branes. The configuration breaks supersymmetry, but the R-R tadpole cancellation conditions are satisfied. A set of three D3-branes at an orbifold fixed point can separate from the point, but when they move perpendicular to the anti-D7-branes put on the fixed point, they are forced to be pulled back due to an attractive interaction between the D3 and anti-D7 branes. In order to stabilize the separation of the D3-branes at nonzero distance, we consider revolution of the D3-branes around the fixed point. Then the gauge symmetry on D3-branes is spontaneously broken, and the rank of the gauge group is reduced. The distance can be set at our will by appropriately choosing the angular momentum of the revolving D3-branes, which should be determined by the initial condition of the cosmological evolution of D-brane configurations. The distance corresponds to the vacuum expectation values of brane moduli fields in the world-volume theory and, if it is written as M/Ms^2 in terms of the string scale Ms, the scale of gauge symmetry breaking is given by M. Angular momentum conservation of revolving D3-branes assures the stability of the scale M against Ms.

Shift symmetry and Higgs inflation in supergravity with observable gravitational waves

We demonstrate how to realize within supergravity a novel chaotic-type inflationary scenario driven by the radial parts of a conjugate pair of Higgs superfields causing the spontaneous breaking of a grand unified gauge symmetry at a scale assuming the value of the supersymmetric grand unification scale. The superpotential is uniquely determined at the renormalizable level by the gauge symmetry and a continuous R symmetry. We select two types of Kahler potentials, which respect these symmetries as well as an approximate shift symmetry. In particular, they include in a logarithm a dominant shift-symmetric term proportional to a parameter c- together with a small term violating this symmetry and characterized by a parameter c+. In both cases, imposing a lower bound on c-, inflation can be attained with subplanckian values of the original inflaton, while the corresponding effective theory respects perturbative unitarity for r+-=c+/c-<1. These inflationary models do not lead to overproduction of cosmic defects, are largely independent of the one-loop radiative corrections and accommodate, for natural values of r+-, observable gravitational waves consistently with all the current observational data. The inflaton mass is mostly confined in the range (3.7-8.1)x10^10 GeV.

On some features of possible torsion effects on observables at Hadron colliders

I give a geometrical description of conformal gauge gravitational theory (CGTG) from the viewpoint of symmetries and affine structure. In the frames of the CGTG incorporating gravitation with torsion space-time into Standard Model of electro-weak interaction (EWI) the multi-muon events produced at the Fermilab Tevatron collider were studied. The CGTG gives the value of the torsion pseudotrace–spinor (muon) universal coupling fT = 4.388 ⋅ 10-17 GF, and with limits from known experiments — torsion mass mT = 0.4700 ⋅ 10-7 eV or mT = 0.445 ⋅ 10-15 muon mass. So the value of the constant of effective four-fermions interaction fT/mT = 0.988, indeed may lead to multi-muon events production. The model of interaction of quantum oscillator with the tensor potential Wμν of traceless part of the torsion lead to 2 cm displacement of quark–lepton system as a whole in the magnetic field of collider in accordance with a significant sample of events related to [Formula: see text] production and decay in which at least one of the muon candidates is produced outside of the beam pipe of radius 1.5 cm. A traceless part of the torsion in CGTG does not vanish in the Newtonian limit of nonzero mass. Torsion gravity potential Wμν gives conservation of a special conformal current and may be produced in the condition of a spontaneous breaking of gauge symmetry where the gravitation mass MX defect is 1–3 Tev ⋅ c-2 or 10-13MX. This effect may be possible at known effects on top pair asymmetries at the Tevatron and LHC and takes place as the known energy dissipation above 3 TeV of the Galaxy gamma-ray and neutrino spectrum from two bubbles outside the Galaxy plane.

On the Trail of the Higgs Boson

I review theoretical issues associated with the Higgs boson and the mystery of spontaneous breaking of the electroweak gauge symmetry. This essay is intended as an introduction to the special issue of Annalen der Physik, “Particle Physics after the Higgs”. image

Formation of a condensate during charged collapse

We observe a condensate forming in the interior of a black hole (BH) during numerical simulations of gravitational collapse of a massless charged (complex) scalar field. The magnitude of the scalar field in the interior tends to a non-zero constant; spontaneous breaking of gauge symmetry occurs and a condensate forms. This phenomena occurs in the presence of a BH without the standard symmetry breaking quartic potential; the breaking occurs via the dynamics of the system itself. We also observe that the scalar field in the interior rotates in the complex plane and show that it matches numerically the electric potential to within 1%. That a charged scalar condensate can form near the horizon of a BH in the Abelian Higgs model without the standard symmetry breaking potential had previously been shown analytically in an explicit model involving a massive scalar field in an AdS4 background. Our numerical simulation lends strong support to this finding, although in our case the scalar field is massless and the spacetime is asymptotically flat.

Hyperscaling violation and electroweak symmetry breaking

We consider a class of simplified models of dynamical electroweak symmetry breaking built in terms of their five-dimensional weakly-coupled gravity duals, in the spirit of bottom-up holography. The sigma-model consists of two abelian gauge bosons and one real, non-charged scalar field coupled to gravity in five dimensions. The scalar potential is a simple exponential function of the scalar field. The background metric resulting from solving the classical equations of motion exhibits hyperscaling violation, at least at asymptotically large values of the radial direction. We study the spectrum of scalar composite states of the putative dual field theory by fluctuating the sigma-model scalars and gravity, and discuss in which cases we find a parametrically light scalar state in the spectrum. We model the spontaneous breaking of the (weakly coupled) gauge symmetry to the diagonal subgroup by the choice of IR boundary conditions. We compute the mass spectrum of spin-1 states, and the precision electroweak parameter S as a function of the hyperscaling coefficient. We find a general bound on the mass of the lightest spin-1 resonance, by requiring that the indirect bounds on the precision parameters be satisfied, that implies that precision electroweak physics excludes the possibility of a techni-rho meson with mass lighter than several TeV.

Growth of Accreting Supermassive Black Hole Seeds and Neutrino Radiation

In the framework of microscopic theory of black hole (MTBH), which explores the most important processes of rearrangement of vacuum state and spontaneous breaking of gravitation gauge symmetry at huge energies, we have undertaken a large series of numerical simulations with the goal to trace an evolution of the mass assembly history of 377 plausible accreting supermassive black hole seeds in active galactic nuclei (AGNs) to the present time and examine the observable signatures today. Given the redshifts, masses, and luminosities of these black holes at present time collected from the literature, we compute the initial redshifts and masses of the corresponding seed black holes. For the present masses MBH/M⊙≃1.1×106 to 1.3×1010 of 377 black holes, the computed intermediate seed masses are ranging from MBHSeed/M⊙≃26.4 to 2.9×105. We also compute the fluxes of ultrahigh energy (UHE) neutrinos produced via simple or modified URCA processes in superdense protomatter nuclei. The AGNs are favored as promising pure UHE neutrino sources, because the computed neutrino fluxes are highly beamed along the plane of accretion disk, peaked at high energies, and collimated in smaller opening angle (θ≪1).

Non-Abelian Gauge Symmetry and the Higgs Mechanism in F-Theory

Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even non-abelian gauge theories have not been fully understood in global F-theory compactifications. We present a systematic discussion of using singularity deformation, which does describe the spontaneous breaking of gauge symmetry in F-theory, to study non-abelian gauge symmetry. Since this branch of the moduli space also exists in the defining M-theory compactification, it provides the only known description of gauge theory states that exists in both pictures; they are string junctions in F-theory. We discuss how global deformations give rise to local deformations, and also give examples where local deformation can be utilized even in models where a global deformation does not exist. Utilizing deformations, we study a number of new examples, including non-perturbative descriptions of SU(3) and SU(2) gauge theories on seven-branes which do not admit a weakly coupled type IIb description. It may be of phenomenological interest that these non-perturbative descriptions do not exist for higher rank SU(N) theories.

Galactic center gamma ray excess in a radiative neutrino mass model

The Fermi gamma ray space telescope data have pointed towards an excess of gamma rays with a peak around 1–3 GeV in the region surrounding the galactic center. This anomalous excess can be described well by a dark matter candidate having mass in the range 31–40 GeV annihilating into bb¯ pairs with a cross section of 〈σv〉≃(1.4–2.0)×10−26 cm3/s. In this work we explore the possibility of having such a dark matter candidate within the framework of a radiative neutrino mass model. The model is a simple extension of the standard model by an additional U(1)X gauge symmetry where the standard model neutrino masses arise both at tree level as well as radiatively by the anomaly free addition of one singlet fermion NR and two triplet fermions Σ1R, Σ2R with suitable Higgs scalars. The spontaneous gauge symmetry breaking is achieved in such a way which results in a residual Z2 symmetry hence providing a stable cold dark matter candidate. We show that the singlet fermionic dark matter candidate in our model can give rise to the galactic center gamma ray excess. The parameter space which simultaneously satisfies the constraints on relic density, direct detection scattering as well as collider bounds essentially corresponds to an s-wave resonance where the gauge boson mass mX is approximately twice that of dark matter mass mχ. We also discuss the compatibility of such a light fermion singlet dark matter with light neutrino mass.