Nonzero Vacuum Expectation Value Research Articles

Twisted holography without conformal symmetry

We discuss the notion of translation-invariant vacua for 2d chiral algebras and relate it to the notion of the associated variety. The two-dimensional chiral algebra associated to four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 U(N) SYM has a conjectural holographic dual involving the B-model topological string theory. We study the effect of non-zero vacuum expectation values on the chiral algebra correlation functions and derive a holographic dual Calabi-Yau geometry. We test our proposal by a large N analysis of correlation functions of determinant operators, whose saddles can be matched with semi-classical configurations of “Giant Graviton” D-branes in the bulk.

Investigating boson sector in an extended standard model with U(1) D symmetry

We have investigated the boson sector in an extended standard model (SM) with additional U(1) D symmetry. In the proposed model, the singlet scalar and doublet scalar Higgs are added in addition to the SM-like scalar Higgs. These scalars are also coupled to the gauge boson fields. In this work, we calculate the masses of both gauge and scalar Higgs bosons. Their masses are obtained through spontaneous symmetry breaking using the Higgs fields with non-zero vacuum expectation values. We also study numerically the positivity conditions of the vacuum expectation value of the scalars. In particular, we perform scanning of the parameter space of the potential and study the obtained scalar mass dependence on the parameter of the model.

Cosmological Bounces Induced by a Fermion Condensate.

We show that it is possible for fermion condensation of the Nambu-Jona-Lasinio type to induce a nonsingular bounce that smoothly connects a phase of slow contraction to a phase of expansion. A chiral condensate-a nonzero vacuum expectation value of the spinor bilinear ⟨Ψ[over ¯]Ψ⟩-can form spontaneously after a slow contraction phase smooths and flattens the universe and the Ricci curvature exceeds a critical value. In this approach, a high density of spin-aligned free fermions is not required, which avoids the problem of generating a large anisotropy and initiating chaotic mixmaster behavior during the bounce phase.

The ℤ2 anomaly in some chiral gauge theories

We revisit the simplest Bars-Yankielowicz (BY) model (the ψη model), starting from a model with an additional Dirac pair of fermions in the fundamental representation, together with a complex color-singlet scalar ϕ coupled to them through a Yukawa interaction. This model possesses a color-flavor-locked 1-form ℤN symmetry, due to the intersection of the color SU(N) and two nonanomalous U(1) groups. In the bulk, the model reduces to the ψη model studied earlier when ϕ acquires a nonzero vacuum expectation value and the extra fermions pair up, get massive and decouple (thus we will call our extended theory as the “X-ray model”), while it provides a regularization of the ℤ2 fluxes needed to study the ℤ2 anomaly. The anomalies involving the 1-form ℤN symmetry reduce, for N even, exactly to the mixed ℤ2 anomaly found earlier in the ψη model. The present work is a first significant step to clarify the meaning of the mixed ℤ2 − [ {mathbb{Z}}_N^{(1)} ]2 anomaly found in the ψη and in other BY and Georgi-Glashow type SU(N) models with even N.

Dark matter in the scotogenic model with spontaneous lepton number violation

Scotogenic models constitute an appealing solution to the generation of neutrino masses and to the dark matter mystery. In this work we consider a version of the Scotogenic model that breaks lepton number spontaneously. At this scope, we extend the particle content of the Scotogenic model with an additional singlet scalar which acquires a non-zero vacuum expectation value and breaks a global lepton number symmetry. As a consequence, a massless Goldstone boson, the majoron, appears in the particle spectrum. We discuss how the presence of the majoron modifies the phenomenology, both in flavor and dark matter observables. We focus on the fermionic dark matter candidate and analyze its relic abundance and prospects for both direct and indirect detection.

Constraining the Lorentz-violating bumblebee vector field with big bang nucleosynthesis and gravitational baryogenesis

By assuming the cosmological principle i.e., an isotropic and homogeneous universe, we consider the cosmology of a vector-tensor theory of gravitation known as the bumblebee model. In this model a single Lorentz-violating timelike vector field with a nonzero vacuum expectation value (VEV) couples to the Ricci tensor and scalar, as well. Taking the ansatz B(t)sim t^beta for the time evolution of the vector field, where beta is a free parameter, we derive the relevant dynamic equations of the Universe. In particular, by employing observational data coming from the Big Bang Nucleosynthesis (BBN) and the matter–antimatter asymmetry in the baryogenesis era, we impose some constraints on the VEV of the bumblebee timelike vector field i.e., xi b^2, and the exponent parameter beta . The former and the latter limit the size of Lorentz violation, and the rate of the time evolution of the background Lorentz-violating bumblebee field, respectively.

Spontaneous Lorentz symmetry breaking effects on GRBs jets arising from neutrino pair annihilation process near a black hole

The study of neutrino pair annihilation into electron-positron pairs (nu {bar{nu }}rightarrow e^-e^+) is astrophysically well-motivated because it is a possible powering mechanism for the gamma-ray bursts (GRBs). In this paper, we estimate the gamma-ray energy deposition rate (EDR) arising from the annihilation of the neutrino pairs in the equatorial plane of a slowly rotating black hole geometry modified by the broken Lorentz symmetry (induced by a background bumblebee vector field). More specifically, owing to the presence of a dimensionless Lorentz symmetry breaking (LSB) parameter l arising from nonminimal coupling between the bumblebee field with nonzero vacuum expectation value and gravity, the metric solution in question differs from the standard slowly rotating Kerr black hole. By idealizing the thin accretion disk temperature profile in the two forms of isothermal and gradient around the bumblebee gravity-based slow rotating black hole, we investigate the influence of spontaneous LSB on the nu {bar{nu }}-annihilation efficiency. For both profiles, we find that positive values of LSB parameter l>0 induce an enhancement of the EDR associated with the neutrino-antineutrino annihilation. Therefore, the process of powering the GRBs jets around bumblebee gravity modified slowly rotating geometry is more efficient in comparison with standard metric. Using the observed gamma-ray luminosity associated with different GRBs types (short, long, and ultra-long), we find, through the analysis of the EDR in the parameter space l-a (a^2ll 1), some allowed ranges for the LSB parameter l.

Holographic model with power-law Maxwell field for color superconductivity

Studying the color superconductivity (CSC) phase is important to understand the physics in the core of the neutron stars which is the only known context where the CSC phase might appear due to the gravitational force squeezing the matter to a sufficiently high density. We propose a simple holographic dual description of the CSC phase transition in the realistic Yang-Mills theory with the power-law Maxwell field. We find the CSC phase transition with the large color number in the deconfinement phase, which is not found in the case of the usual Maxwell field, if the power parameter characterizing for the power-law Maxwell field is sufficiently lower than one but above $1/2$ and the chemical potential is above a critical value. However, the power parameter is not arbitrary below one because when this parameter is sufficiently far away from one it leads to the occurrence of the CSC state in the confinement phase which is not compatible with a nonzero vacuum expectation value of the color nonsinglet operator.

Spontaneous conformal symmetry breaking and quantum quadratic gravity

We investigate several quantum phenomena related to quadratic gravity after rewriting the general fourth-order action in a more convenient form that is second order in derivatives and produces only first-class constraints in phase space. We find that a Higgs mechanism may occur in the conformally invariant subset of the general quadratic action if the theory is conformally coupled to a scalar field that acquires a nonzero vacuum expectation value and spontaneously breaks the conformal symmetry. Then, in the broken phase, the originally massless spin-2 ghost may absorb both the scalar and vector fields to become massive. We also perform a Becchi-Rouet-Stora-Tyutin quantization of second-order quadratic gravity in the covariant operator formalism and discuss conditions under which unitarity of the full interacting quantum theory may be established.

Heavier W boson, dark matter, and gravitational waves from strings in an SO(10) axion model

Inspired by the recent determination of the $W$-boson mass by the CDF collaboration, we revisit an $SO(10)$ axion model in which a scalar $SU(2{)}_{L}$ triplet field with zero hypercharge is known to acquire a nonzero vacuum expectation value (VEV) through its mixing with the Standard Model Higgs doublet. The triplet VEV provides a sizable contribution to the $W$ mass, which helps in significantly lowering the $7\ensuremath{\sigma}$ discrepancy between the Standard Model prediction and the higher CDF value for ${m}_{W}$. We show that the relatively light triplet mass ($\ensuremath{\sim}(1--50)\text{ }\text{ }\mathrm{TeV}$) is compatible with gauge coupling unification and observable proton decay. An unbroken ${Z}_{2}$ gauge symmetry, coupled with the presence of two fermionic 10-plets required to resolve the axion domain wall problem means that both axions and a stable intermediate mass ($\ensuremath{\sim}{10}^{9}--{10}^{10}\text{ }\text{ }\mathrm{GeV}$) fermion are plausible dark matter candidates. We also display the gravitational wave spectrum from the intermediate scale topologically stable cosmic strings predicted by the model.

Changing patterns in electroweak precision fits with new color-charged states: Oblique corrections and the W -boson mass

The recent measurement by the CDF Collaboration of the $W$ boson mass is in significant tension with the Standard Model expectation, showing a discrepancy of seven standard deviations. A larger value of $m_W$ affects the global electroweak fit, particularly the best-fit values of the Peskin-Takeuchi parameters $S$, $T$ (and perhaps $U$) that measure oblique corrections from new physics. To meet this challenge, we propose some simple models capable of generating non-negative $S$ and $T$, the latter of which faces the greatest upward pressure from the CDF measurement in scenarios with $U=0$. Our models feature weak multiplets of scalars charged under $\mathrm{SU}(3)_{\text{c}} \times \mathrm{U}(1)_Y$, which cannot attain nonzero vacuum expectation values but nevertheless produce e.g. $T \neq 0$ given some other mechanism to split the electrically charged and neutral scalars. We compute the oblique corrections in these models and identify ample parameter space supporting the CDF value of $m_W$.

Gauge symmetry breaking in flux compactification with a Wilson-line scalar condensate

We discuss the gauge symmetry breaking of six dimensional theories in flux compactification with a magnetic flux background and a constant vacuum expectation value (VEV) for the scalar fields, which are zero modes of extra spatial components of the gauge field. Although the effective potential for the scalar fields are known not to be generated classically and radiatively in a magnetic flux background only, the one-loop effective potential is shown to be generated by the effects of the non-zero constant VEV. As illustrations, we calculate the one-loop effective potential in SU(2) and SU(3) Yang-Mills theories. In both cases, we find that the potential minimum is located at non-zero VEV and the gauge symmetry breaking takes place.

Exact modifications on a vacuum spacetime due to a gradient bumblebee field at its vacuum expectation value

This work belongs to the context of the standard-model extension, in which a Lorentz symmetry violation is induced by a bumblebee field as it acquires a nonzero vacuum expectation value. The mathematical formulation of a generic bumblebee model and its associated dynamical equations are presented. Then, these equations are considered for the vacuum and a substantial simplification is performed for the particular case of a gradient bumblebee field at its vacuum expectation value. After some further manipulation, a method to easily find solutions to the model is developed, in which the exact effect on the spacetime description due to the presence of this bumblebee field is explicitly provided. As some examples, the method is applied to determine the implications of the bumblebee field on the Schwarzschild spacetime and also on a rotating one. A previously published solution is recovered and some new ones are obtained. In the rotating situation, a simple solution is found which contains both the Kerr solution and the already published one as special cases. It is also shown its distinguished surfaces are still given by the same corresponding expressions for the Kerr solution. In conclusion, the mathematical improvement made is considered to be a significant contribution to the theory as a powerful tool to investigate its many aspects and consequences.

Gravitational waves detectable in laser interferometers from axion-SU(2) inflation

Chromo-natural inflation (CNI) is an inflationary model where an axion coupled with SU(2) gauge fields acts as the inflaton. In CNI, the gauge fields have nonzero vacuum expectation values (VEVs), which results in the enhancement of gravitational waves (GWs). The original CNI is ruled out by the Planck observations due to the overproduction of GWs. In this work, we consider an inflationary model where the gauge fields acquire nonzero VEVs after the CMB modes exit the horizon. Moreover, we add to the model another field that dominates the universe and drives inflation after the axion starts to oscillate and the gauge field VEVs vanish. By performing numerical simulations, we find a parameter space where the enhanced GWs do not violate the CMB constraints and can be detected by the future GWs observations such as BBO and ET.

Pair production of neutral Higgs particles in the B-LSSM

Higgs pair production provides a unique handle for measuring the strength of Higgs self interaction and constraining the shape of the Higgs potential. Including radiative corrections to the trilinear couplings of CP-even Higgs, we investigate the cross section of the lightest neutral Higgs pair production in gluon fusion at the Large Hadron Collider in the supersymmetric extensions of the standard model. Numerical results indicate that the correction to the cross section is about 11% in the B-LSSM, while is only about 4% in the MSSM. Considering the constraints of the experimental data of the lightest Higgs, we find that the gauge couplings of U(1) B–L and the ratio of the nonzero vacuum expectation values of two singlets also affect strongly the theoretical evaluations on the production cross section in the B-LSSM.

Type-II seesaw triplet scalar effects on neutrino trident scattering

In Type-II seesaw model, an electroweak triplet scalar field Δ with a non-zero vacuum expectation value (vev) vΔ is introduced to facilitate the generation of small neutrino masses. A non-zero vΔ also affects the W mass through the electroweak ρ parameter, making it to be less than 1 as predicted by standard model (SM). The component fields in Δ come along introduce additional contributions to reduce the SM rare neutrino trident scattering cross section. These fields also induce new processes not existed in SM, such as li→lj‾lkll and li→ljγ. There are severe constraints on these processes which limit the effects on neutrino trident scattering and the ρ parameter and therefore the W mass. The newly measured W mass by CDF makes the central value of ρ parameter to be larger than 1, even larger than previously expected. Combining neutrinoless double beta decay, direct neutrino mass and oscillation data, we find a lower limit for vΔ as a function of the triplet scalar mass mΔ, vΔ>(6.3∼8.4)eV(100GeV/mΔ). To have significant effect on ρ in this model, vΔ needs to be in the range of a GeV or so. However this implies a very small mΔ which is ruled out by data. We conclude that the effect of triplet vev vΔ on the W mass can be neglected. We also find that at 3σ level, the deviation of the ratio for Type-II Seesaw to SM neutrino trident scattering cross section predictions is reduced to be below 1, but is restricted to be larger than 0.98.

Loop-induced h → γγ, Zγ, gg decays in 3-Higgs doublet models

In this paper, we analyze the loop-induced decays of neutral Higgs boson [Formula: see text] into pairs of photons, gluons and [Formula: see text] in 3-Higgs Doublet Models (3HDMs), where all the doublets have nonzero vacuum expectation values. In the 3HDM, there are contributions to these decays from loops of charged scalars [Formula: see text] that are not present in the Standard Model. We find an enhancement in the channel [Formula: see text] with respect to the Standard Model prediction in some parameter region while respecting constraints from the measurements of [Formula: see text] at the LHC. The charged Higgs bosons [Formula: see text] lead to the enhancement of [Formula: see text] decay mode in some part of the parameter space of the 3HDM. Then, we discuss the correlations between the decay modes [Formula: see text] and [Formula: see text]. Moreover, we study Type-I and Type-Z of 3HDMs and find that these types of 3HDMs can be distinguished via only the gluonic decays, since the contributions of the [Formula: see text] loops are dominant to those of fermion loops. We also investigate the effects of the model parameters on these loop-induced decays. As an interesting phenomenological consequence, the 3HDM is dominantly governed by the parameters: two ratios of vacuum expectation values (VEVs); [Formula: see text], [Formula: see text] and the mixing angles of the CP-even Higgs bosons, [Formula: see text] and [Formula: see text].

Analyses of scalar potential and lepton flavor violating decays in a model with A4 symmetry

We have considered a model, originally proposed by Ma and Wegman, where the mixing pattern in neutrino sector is explained with three Higgs doublets, six Higgs triplets and A4 symmetry. The mixing pattern is explained with the help of vacuum expectation values (VEVs) of the above mentioned doublets and triplets. In order to study about the VEVs of the scalar fields, we construct the full invariant scalar potential of this model. After minimizing this scalar potential, we have found that two Higgs triplets can acquire zero VEVs. In order to generate non-zero VEVs to all the six Higgs triplets, we have added two more Higgs doublets to the model. Thereafter we have demonstrated that the current neutrino oscillation data can be consistently explained in our model. To study some phenomenological implications of this model, we have worked out on the branching ratios for lepton flavor violating decays.

Scale invariant FIMP miracle

We study the freeze-in production of vector dark matter (DM) in a classically scale invariant theory, where the Standard Model (SM) is augmented with an abelian U(1) X gauge symmetry that is spontaneously broken due to the non-zero vacuum expectation value (VEV) of a scalar charged under the U(1) X . Generating the SM Higgs mass at 1-loop level, it leaves only two parameters in the dark sector, namely, the DM mass mX and the gauge coupling gX as independent, and supplement with a naturally light dark scalar particle. We show, for gX ~ \U0001d4aa(10-5), it is possible to produce the DM X out-of-equilibrium in the early Universe, satisfying the observed relic abundance for mX ~ \U0001d4aa(TeV), which in turn also determines the scalar mixing angle sinθ ~ \U0001d4aa(10-5). The presence of such naturally light scalar mediator with tiny mixing with the SM,opens up the possibility for the model to be explored in direct search experiment, which otherwise is insensitive to standard freeze-in scenarios. Moreover we show that even with such feeble couplings, necessary for the DM freeze-in, the scenario is testable in several light dark sector searches (e.g., in DUNE and in FASER-II),satisfying constraints from the observed relic abundance as well as big bang nucleosynthesis (BBN). Particularly, we find, regions in the parameter space with mX ≳ 1.8 TeV becomes insensitive to direct detection probe but still can be accessible in lifetime frontier searches, again courtesy to the underlying scale invariance of the theory.

Magnetic reconnection and energy extraction from a spinning black hole with broken Lorentz symmetry

In the Penrose process and the Blandford-Znajek mechanism, the rotational energy of a black hole (BH) is extracted via particle fission and magnetic tension, respectively. Recently, inspired by a fundamental trait in plasma astrophysics known as magnetic reconnection (MR), a new energy extraction mechanism based on the fast reconnection of the magnetic field lines inside the ergosphere has been proposed by Comisso and Asenjo. In this paper, we investigate energy extraction caused by MR in the ergosphere of a rapidly spinning BH with broken Lorentz symmetry by a background bumblebee vector field. The desired rotating BH solution differentiates from the standard Kerr BH via the Lorentz symmetry breaking (LSB) parameter $l$, which comes from nonminimal coupling between the bumblebee field with nonzero vacuum expectation value and gravity. We find that incorporating $l<0$ in the background is in the interest of the energy extraction via MR for the fast-spinning BH surrounded by the plasma with weak magnetization, below what is expected from the scenario by Comisso and Asenjo. Our analysis robustly indicates that the power of energy extraction and efficiency of the plasma energization process through fast MR is more efficient than the Comisso-Asenjo solution, provided that the LSB parameter is negative, $l<0$. Compared to the Blandford-Znajek mechanism arising from the underlying background, we also show that MR is a more efficient energy extraction mechanism if $l<0$.